Juha Heinonen's Books

Sobolev Spaces on Metric Measure Spaces

By: Juha Heinonen,Pekka Koskela,Nageswari Shanmugalingam,Jeremy T. Tyson

Write a review Read reviews Take a Quiz Solve Book Puzzle

Sobolev Spaces on Metric Measure Spaces

By: Juha Heinonen,Pekka Koskela,Nageswari Shanmugalingam,Jeremy T. Tyson

This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

447

Publisher

Cambridge University Press

Published Date

ISBN 10

1107092345

ISBN 13

9781107092341

Nonlinear Potential Theory of Degenerate Elliptic Equations

By: Juha Heinonen,Tero Kipelainen,Olli Martio

Write a review Read reviews Take a Quiz Solve Book Puzzle

Nonlinear Potential Theory of Degenerate Elliptic Equations

By: Juha Heinonen,Tero Kipelainen,Olli Martio

A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

417

Publisher

Courier Dover Publications

Published Date

ISBN 10

0486830462

ISBN 13

9780486830469

Lectures on Analysis on Metric Spaces

By: Juha Heinonen

Write a review Read reviews Take a Quiz Solve Book Puzzle

Lectures on Analysis on Metric Spaces

By: Juha Heinonen

The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is recent and appears for the first time in book format.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

149

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461301319

ISBN 13

9781461301318

Maximal Function Methods for Sobolev Spaces

By: Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas

Write a review Read reviews Take a Quiz Solve Book Puzzle

Maximal Function Methods for Sobolev Spaces

By: Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas

This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

354

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470465752

ISBN 13

9781470465759

Quantum Measurement

By: Paul Busch,Pekka Lahti,Juha-Pekka Pellonpää,Kari Ylinen

Write a review Read reviews Take a Quiz Solve Book Puzzle

Quantum Measurement

By: Paul Busch,Pekka Lahti,Juha-Pekka Pellonpää,Kari Ylinen

This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann’s classic treatise with this title. Fundamental non-classical features of quantum mechanics—indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality—are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4. Foundations discusses a selection of foundational topics (quantum-classical contrast, Bell nonlocality, measurement limitations, measurement problem, operational axioms) from a measurement theoretic perspective. The book is addressed to physicists, mathematicians and philosophers of physics with an interest in the mathematical and conceptual foundations of quantum physics, specifically from the perspective of measurement theory.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

544

Publisher

Springer

Published Date

ISBN 10

331943389X

ISBN 13

9783319433899

Children in the Information Society

The Case of Finland

By: Juha Suoranta,Hanna Lehtimäki

Write a review Read reviews Take a Quiz Solve Book Puzzle

Children in the Information Society

The Case of Finland

By: Juha Suoranta,Hanna Lehtimäki

Finland is known worldwide as a laboratory of the information society. The Finnish model combines information technology know-how with welfare state structures where equality seems to prevail. Can we take this picture at face value, or is it too optimistic? In this book we approach the case of Finland from children's perspectives by exploring what ICTs (information and communication technology) and media they use, how they use them, and what their thoughts are concerning this use? How does media become a part of children's everyday lives? The book is based on a nationally representative child survey supplemented by interviews where eight- to ten-year old Finnish children have been the key informants.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

172

Publisher

Peter Lang

Published Date

ISBN 10

0820468290

ISBN 13

9780820468297

Lectures on Analysis on Metric Spaces

By: Juha Heinonen

Write a review Read reviews Take a Quiz Solve Book Puzzle

Lectures on Analysis on Metric Spaces

By: Juha Heinonen

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

158

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387951040

ISBN 13

9780387951041

Sobolev Spaces on Metric Measure Spaces

An Approach Based on Upper Gradients

By: Juha Heinonen,Pekka Koskela,Nageswari Shanmugalingam,Jeremy T. Tyson

Write a review Read reviews Take a Quiz Solve Book Puzzle

Sobolev Spaces on Metric Measure Spaces

An Approach Based on Upper Gradients

By: Juha Heinonen,Pekka Koskela,Nageswari Shanmugalingam,Jeremy T. Tyson

Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of metric measure spaces supporting a Poincaré inequality. This coherent treatment from first principles is an ideal introduction to the subject for graduate students and a useful reference for experts. It presents the foundations of the theory of such first-order Sobolev spaces, then explores geometric implications of the critical Poincaré inequality, and indicates numerous examples of spaces satisfying this axiom. A distinguishing feature of the book is its focus on vector-valued Sobolev spaces. The final chapters include proofs of several landmark theorems, including Cheeger's stability theorem for Poincaré inequalities under Gromov–Hausdorff convergence, and the Keith–Zhong self-improvement theorem for Poincaré inequalities.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

447

Publisher

Cambridge University Press

Published Date

ISBN 10

1316241033

ISBN 13

9781316241035

Nonlinear Potential Theory of Degenerate Elliptic Equations

By: Juha Heinonen,Tero Kipelainen,Olli Martio

Write a review Read reviews Take a Quiz Solve Book Puzzle

Nonlinear Potential Theory of Degenerate Elliptic Equations

By: Juha Heinonen,Tero Kipelainen,Olli Martio

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

417

Publisher

Courier Dover Publications

Published Date

ISBN 10

0486830462

ISBN 13

9780486830469

Book's by Juha Heinonen

Sobolev Spaces on Metric Measure Spaces

Sobolev Spaces on Metric Measure Spaces

Nonlinear Potential Theory of Degenerate Elliptic Equations

Nonlinear Potential Theory of Degenerate Elliptic Equations

Lectures on Analysis on Metric Spaces

Lectures on Analysis on Metric Spaces

Maximal Function Methods for Sobolev Spaces

Maximal Function Methods for Sobolev Spaces

Quantum Measurement

Quantum Measurement

Children in the Information Society

Children in the Information Society

Lectures on Analysis on Metric Spaces

Lectures on Analysis on Metric Spaces

Sobolev Spaces on Metric Measure Spaces

Sobolev Spaces on Metric Measure Spaces

Nonlinear Potential Theory of Degenerate Elliptic Equations

Nonlinear Potential Theory of Degenerate Elliptic Equations

Username

Password

Username

Password

Password again

Birthday

Email