Alexander Volberg's Books

The Bellman Function Technique in Harmonic Analysis

By: Vasily Vasyunin,Alexander Volberg

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The Bellman Function Technique in Harmonic Analysis

By: Vasily Vasyunin,Alexander Volberg

A comprehensive reference on the Bellman function method and its applications to various topics in probability and harmonic analysis.

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Page Count

465

Publisher

Cambridge University Press

Published Date

ISBN 10

1108486894

ISBN 13

9781108486897

Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces

By: Alexander Volberg

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Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces

By: Alexander Volberg

Singular integral operators play a central role in modern harmonic analysis. Simplest examples of singular kernels are given by Calderon-Zygmund kernels. Many important properties of singular integrals have been thoroughly studied for Calderon-Zygmund operators. In the 1980's and early 1990's, Coifman, Weiss, and Christ noticed that the theory of Calderon-Zygmund operators can be generalized from Euclidean spaces to spaces of homogeneous type. The purpose of this book is to make the reader believe that homogeneity (previously considered as a cornerstone of the theory) is not needed. This claim is illustrated by presenting two harmonic analysis problems famous for their difficulty. The first problem treats semiadditivity of analytic and Lipschitz harmonic capacities. The volume presents the first self-contained and unified proof of the semiadditivity of these capacities. The book details Tolsa's solution of Painleve's and Vitushkin's problems and explains why these are problems of the theory of Calderon-Zygmund operators on nonhomogeneous spaces. The exposition is not dimension-specific, which allows the author to treat Lipschitz harmonic capacity and analytic capacity at the same time. The second problem considered in the volume is a two-weight estimate for the Hilbert transform. This problem recently found important applications in operator theory, where it is intimately related to spectral theory of small perturbations of unitary operators. The book presents a technique that can be helpful in overcoming rather bad degeneracies (i.e., exponential growth or decay) of underlying measure (volume) on the space where the singular integral operator is considered. These situations occur, for example, in boundary value problems for elliptic PDE's in domains with extremely singular boundaries. Another example involves harmonic analysis on the boundaries of pseudoconvex domains that goes beyond the scope of Carnot-Caratheodory spaces. The book is suitable for graduate students and research mathematicians interested in harmonic analysis.

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Page Count

176

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821832522

ISBN 13

9780821832523

Russian Mathematics Education

History and World Significance

By: Alexander Karp,Bruce Ramon Vogeli

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Russian Mathematics Education

History and World Significance

By: Alexander Karp,Bruce Ramon Vogeli

Volume I, entitled Russian Mathematics Education: History and World Significance, consists of several chapters written by distinguished authorities from Russia, the United States and other nations. It Examines the hostory of mathematics education in Russia and its relevance to mathematics education throughout the world. The second volume, entitled Russian Mathematics education is highly respected for its achievements and was once very influential internationally, it has never been explored in depth. This publication does just that. --Book Jacket.

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Page Count

398

Publisher

World Scientific

Published Date

ISBN 10

9814277053

ISBN 13

9789814277051

Bounded and Compact Integral Operators

By: David E. Edmunds,V.M Kokilashvili,Alexander Meskhi

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Bounded and Compact Integral Operators

By: David E. Edmunds,V.M Kokilashvili,Alexander Meskhi

The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness).

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Page Count

655

Publisher

Springer Science & Business Media

Published Date

ISBN 10

940159922X

ISBN 13

9789401599221

Clinical Neuropsychology and Cognitive Neurology of Parkinson's Disease and Other Movement Disorders

By: Alexander I. Troster

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Clinical Neuropsychology and Cognitive Neurology of Parkinson's Disease and Other Movement Disorders

By: Alexander I. Troster

The book provides an up-to-date account of the neuropsychological, cognitive-neurological, and neuropsychiatric aspects of movement disorders. The past ten years have seen an explosion of research covering non-motor aspects of Parkinson's disease and, more recently, movement disorders such as essential tremor, dystonia, corticobasal syndrome, progressive supranuclear palsy, and multiple system atrophy. It is often these neurobehavioral features that become troubling to the patient: they are sometimes difficult to recognize and treat, are associated with diminished patient and caregiver quality of life, and may hasten disease progression, loss of independence, and institutionalization. This book discusses the most recent diagnostic and treatment guidelines for such cognitive and psychiatric conditions in Parkinson's disease and other movement disorders, while providing practical tips and strategies for general assessment. The rapid accumulation of research in this field makes it increasingly difficult for one or two people to author a comprehensive text in an expert manner. The world-class team assembled for this volume succeeds in covering widely diverse areas such as the pathology, neuroimaging, assessment, and treatment of an ever-growing set of neurobehavioral features of movement disorders -- cognitive impairment and dementia, depression, apathy, anxiety, psychosis, and impulse control disorders. The text also surveys fundamental knowledge about basal ganglia function and dysfunction, assessment and evaluation techniques applicable to a range of movement disorders, and quality of life issues more broadly.

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Page Count

561

Publisher

Oxford University Press

Published Date

ISBN 10

0199812381

ISBN 13

9780199812387

Battling Nell

The Life of Southern Journalist Cornelia Battle Lewis, 1893--1956

By: Alexander S. Leidholdt

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Battling Nell

The Life of Southern Journalist Cornelia Battle Lewis, 1893--1956

By: Alexander S. Leidholdt

A longtime columnist for the Raleigh News and Observer, Cornelia Battle Lewis earned a national reputation in the 1920s and 1930s for her courageous advocacy on behalf of women's rights, African Americans, children, and labor unions. Late in her life, however, after fighting mental illness, Lewis reversed many of her stances and railed against the liberalism she had spent her life advancing. In Battling Nell, Alexander S. Leidholdt tells the compelling and ultimately tragic life story of this groundbreaking journalist against the backdrop of the turbulent post-Reconstruction Jim Crow South and speculates about the cause of her extraordinary transformation. The daughter of North Carolina's most prominent public health official, Lewis grew up in Raleigh, but her experiences at Smith College in Massachusetts, and later in France during World War I, led her to question the prevailing racial attitudes and gender roles of her native region. In 1920, Lewis began her storied career with the News and Observer. Inspired by H. L. Mencken's scathing criticism of the South, she soon established herself as the region's leading female liberal journalist. Her column, "Incidentally," attacked the Ku Klux Klan, lobbied against the exploitation of mill workers, defended strikers during the notorious communist-organized Gastonia labor violence, mocked religious fundamentalists who fought the teaching of evolution, and decried lynch law. A suffragist and a feminist who saw women's rights as inextricably linked to human rights, Lewis ran for state legislature in 1928 and was one of the first women in North Carolina to be admitted to the bar. In the 1930s, however, Lewis faced repeated institutionalizations for a debilitating bout of mental illness and sought treatment from Christian Science practitioners, spiritualists, and psychotherapists. As she aged, her views grew increasingly reactionary, and she insisted that she had served as a communist dupe during the Gastonia strike and trials, that communists had infiltrated the University of North Carolina, and that many of her former progressive allies had ties to communism. Finally, many of her opinions completely reversed, and in the wake of the 1954 Brown v. Board decision, she served as an influential spokesperson for the South's massive resistance to public school desegregation. She continued to espouse these conservative beliefs until her death in 1956. In his detailed retelling of Lewis's fascinating life, Leidholdt chronicles the turbulent history of North Carolina from the 1920s through the 1950s, as industrialization and racial integration began to tear at the region's conservative fabric. He vividly explains the background and ramifications of Lewis's many controversial stances and explores the possible reasons for her ideological about-face. Through the extraordinary story of "Battling Nell," Leidholdt reveals how the complex issues of gender, labor, and race intertwined to influence the convulsive events that shaped the course of early twentieth-century southern history.

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Page Count

352

Publisher

LSU Press

Published Date

ISBN 10

0807136700

ISBN 13

9780807136706

An Introduction to Infinite-Dimensional Differential Geometry

By: Alexander Schmeding

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An Introduction to Infinite-Dimensional Differential Geometry

By: Alexander Schmeding

Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core.

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Page Count

284

Publisher

Cambridge University Press

Published Date

ISBN 10

1009089307

ISBN 13

9781009089302

Attrition in the Pharmaceutical Industry

Reasons, Implications, and Pathways Forward

By: Alexander Alex,C. John Harris,Dennis A. Smith

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Attrition in the Pharmaceutical Industry

Reasons, Implications, and Pathways Forward

By: Alexander Alex,C. John Harris,Dennis A. Smith

With a focus on case studies of R&D programs in a variety of disease areas, the book highlights fundamental productivity issues the pharmaceutical industry has been facing and explores potential ways of improving research effectiveness and efficiency. Takes a comprehensive and holistic approach to the problems and potential solutions to drug compound attrition Tackles a problem that adds billions of dollars to drug development programs and health care costs Guides discovery and development scientists through R&D stages, teaching requirements and reasons why drugs can fail Discusses potential ways forward utilizing new approaches and opportunities to reduce attrition

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Page Count

370

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118679679

ISBN 13

9781118679678

Editor for Justice

The Life of Louis I. Jaffé

By: Alexander S. Leidholdt

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Editor for Justice

The Life of Louis I. Jaffé

By: Alexander S. Leidholdt

From his assumption of the Norfolk Virginian-Pilot's editorial helm in 1919 until his death in 1950, Louis Isaac Jaffé served as one of the South's leading and most respected liberal journalists. Prejudice he faced as a Jew created in him an abiding empathy with the downtrodden, and his World War I military service and subsequent Red Cross work deepened his sensitivity to injustice. Alexander Leidholdt's new biography maps the battlefield of intolerance and civil rights violations on which Jaffé fired his journalistic salvos and explores the complexities of a man who was poised to become a national spokesman for a better South. Jaffé worked ceaselessly to advance racial understanding, successfully lobbying locally for black parks and beaches, black police, and a black college. A high point of Leidholdt's book is the account of Jaffé's attacks on mob justice, a stirring record of one writer's response to what he saw as inexcusable moral sluggishness in civil authorities. For his campaign urging Virginia lawmakers to adopt stiff antilynching legislation, he earned the 1929 Pulitzer Prize for distinguished editorial writing. Achieving a poignant balance between Jaffé's significant professional accomplishments and the private pains he bore—including anti-Semitism, a mentally unstable wife, and an estranged son—this superb study demonstrates how Jaffé's difficulties limited him as an active liberal reformer but also fueled his prescient and impassioned warnings against Hitler's rise to power in the early thirties. Drawing extensively from primary source material, much of it previously unexamined, Editor for Justice makes an important contribution to journalism and to southern, Jewish, and black history. Readers will treasure the depiction of an extraordinary champion of human rights.

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Page Count

532

Publisher

LSU Press

Published Date

ISBN 10

0807127515

ISBN 13

9780807127513

Integral Operators in Non-Standard Function Spaces

Volume 1: Variable Exponent Lebesgue and Amalgam Spaces

By: Vakhtang Kokilashvili,Alexander Meskhi,Humberto Rafeiro,Stefan Samko

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Integral Operators in Non-Standard Function Spaces

Volume 1: Variable Exponent Lebesgue and Amalgam Spaces

By: Vakhtang Kokilashvili,Alexander Meskhi,Humberto Rafeiro,Stefan Samko

This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.

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Page Count

585

Publisher

Birkhäuser

Published Date

ISBN 10

3319210157

ISBN 13

9783319210155

Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces

By: Alexander Volberg

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Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces

By: Alexander Volberg

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Page Count

176

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821832522

ISBN 13

9780821832523

Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces

By: Alexander Volberg

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Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces

By: Alexander Volberg

Singular integral operators play the central part in modern harmonic analysis. Simplest examples of singular kernels are given by Calderón-Zygmund kernels. Many important properties of singular integrals have been thoroughly studied for Calderón-Zygmund operators. In the '80s and early '90s, Coifman, Weiss, and Christ noticed that the theory of Calderón-Zygmund operators can be generalized from Euclidean spaces to spaces of homogeneous type. The purpose of this book is to make the reader believe that homogeneity (previously considered as a cornerstone of the theory) is not needed. This claim i.

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Page Count

167

Published Date

ISBN 10

1470424614

ISBN 13

9781470424619

Book's by Alexander Volberg

The Bellman Function Technique in Harmonic Analysis

The Bellman Function Technique in Harmonic Analysis

Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces

Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces

Russian Mathematics Education

Russian Mathematics Education

Bounded and Compact Integral Operators

Bounded and Compact Integral Operators

Clinical Neuropsychology and Cognitive Neurology of Parkinson's Disease and Other Movement Disorders

Clinical Neuropsychology and Cognitive Neurology of Parkinson's Disease and Other Movement Disorders

Battling Nell

Battling Nell

An Introduction to Infinite-Dimensional Differential Geometry

An Introduction to Infinite-Dimensional Differential Geometry

Attrition in the Pharmaceutical Industry

Attrition in the Pharmaceutical Industry

Editor for Justice

Editor for Justice

Integral Operators in Non-Standard Function Spaces

Integral Operators in Non-Standard Function Spaces

Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces

Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces

Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces

Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces

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