J.L. Doob's Books

Classical Potential Theory and Its Probabilistic Counterpart

Advanced Problems

By: J. L. Doob

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Classical Potential Theory and Its Probabilistic Counterpart

Advanced Problems

By: J. L. Doob

Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject to domination principles (inequalities) involving the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping (balayage) of the measures associated with potentials, and so on.

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Page Count

865

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461252083

ISBN 13

9781461252085

Measure Theory

By: J.L. Doob

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Measure Theory

By: J.L. Doob

This text is unique in accepting probability theory as an essential part of measure theory. Therefore, many examples are taken from probability, and probabilistic concepts such as independence and Markov processes are integrated into the text. Also, more attention than usual is paid to the role of algebras, and the metric defining the distance between sets as the measure of their symmetric difference is exploited more than is customary.

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Page Count

219

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Springer Science & Business Media

Published Date

ISBN 10

1461208777

ISBN 13

9781461208778

Interpolation and Approximation by Rational Functions in the Complex Domain

By: J. L. Walsh

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Interpolation and Approximation by Rational Functions in the Complex Domain

By: J. L. Walsh

The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.

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Page Count

418

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821810200

ISBN 13

9780821810200

A Festschrift For Erich L. Lehmann

By: Peter .J. Bickel,K. Doksum,J.L. Hodges

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A Festschrift For Erich L. Lehmann

By: Peter .J. Bickel,K. Doksum,J.L. Hodges

A collection of essays and articles In honour of Erich. L. Lehmann's sixty-fifth birthday. Including works on Vector Autoregressive models, Bootstrapping Regression Models, Bootstrapping Regression Models and Estimation of the Mean or Total when Measurement Protocols.

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Page Count

478

Publisher

CRC Press

Published Date

ISBN 10

0534980449

ISBN 13

9780534980443

American Cobra Pilot

A Marine Remembers a Dog and Pony Show

By: Capt. J.L. Groom

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American Cobra Pilot

A Marine Remembers a Dog and Pony Show

By: Capt. J.L. Groom

Think the Marine Corps is a war-fighting organization? Think again. A Marine Cobra helicopter pilot finds himself off the coast of Korea taking part in a political exercise known as Ssang Young. The goal is to conduct a Marine amphibious landing. However, Captain Groom soon learns amphibious assault in practice is a dog and pony show parade, the likes of which even the Westminster dog show would envy. The following tale covers one Marine pilots journey through the lead-up, execution, and aftermath of this epic tale in the pivot, uh, I mean shift, to the Pacific. Pivot means we turn our backs. It was replaced with shift.

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Page Count

292

Publisher

Xlibris Corporation

Published Date

ISBN 10

151445940X

ISBN 13

9781514459409

Inequalities in Mechanics and Physics

By: G. Duvant,J. L. Lions

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Inequalities in Mechanics and Physics

By: G. Duvant,J. L. Lions

1. We begin by giving a simple example of a partial differential inequality that occurs in an elementary physics problem. We consider a fluid with pressure u(x, t) at the point x at the instant t that 3 occupies a region Q oflR bounded by a membrane r of negligible thickness that, however, is semi-permeable, i. e., a membrane that permits the fluid to enter Q freely but that prevents all outflow of fluid. One can prove then (cf. the details in Chapter 1, Section 2.2.1) that au (aZu azu aZu) (1) in Q, t>o, -a - du = g du = -a z + -a z + -a z t Xl X X3 z l g a given function, with boundary conditions in the form of inequalities u(X,t»o => au(x,t)/an=O, XEr, (2) u(x,t)=o => au(x,t)/an?:O, XEr, to which is added the initial condition (3) u(x,O)=uo(x). We note that conditions (2) are non linear; they imply that, at each fixed instant t, there exist on r two regions r~ and n where u(x, t) =0 and au (x, t)/an = 0, respectively. These regions are not prescribed; thus we deal with a "free boundary" problem.

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Page Count

415

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642661653

ISBN 13

9783642661655

Groups and Representations

By: J.L. Alperin,Rowen B. Bell

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Groups and Representations

By: J.L. Alperin,Rowen B. Bell

A concise treatment of topics from group theory and representation theory for use in a one-term course. Focussing on the non-commutative side of the field, this advanced textbook emphasizes the general linear group as the most important group and example. Readers are expected to be familiar with groups, rings, and fields, and to have a solid knowledge of linear algebra. Close to 200 exercises of varying difficulty serve both to reinforce the main concept of the text and to introduce the reader to additional topics.

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200

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461207991

ISBN 13

9781461207993

Applications of the Theory of Matrices

By: F. R. Gantmacher,J.L. Brenner

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Applications of the Theory of Matrices

By: F. R. Gantmacher,J.L. Brenner

The breadth of matrix theory's applications is reflected by this volume, which features material of interest to applied mathematicians as well as to control engineers studying stability of a servo-mechanism and numerical analysts evaluating the roots of a polynomial. Starting with a survey of complex symmetric, antisymmetric, and orthogonal matrices, the text advances to explorations of singular bundles of matrices and matrices with nonnegative elements. Applied mathematicians will take particular note of the full and readable chapter on applications of matrix theory to the study of systems of linear differential equations, and the text concludes with an exposition on the Routh-Hurwitz problem plus several helpful appendixes. 1959 edition.

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Page Count

336

Publisher

Courier Corporation

Published Date

ISBN 10

0486445542

ISBN 13

9780486445540

Classical Potential Theory and Its Probabilistic Counterpart

Advanced Problems

By: J. L. Doob

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Classical Potential Theory and Its Probabilistic Counterpart

Advanced Problems

By: J. L. Doob

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Solve jigsaw puzzle

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Page Count

898

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387908811

ISBN 13

9780387908816

Book's by J.L. Doob

Classical Potential Theory and Its Probabilistic Counterpart

Classical Potential Theory and Its Probabilistic Counterpart

Measure Theory

Measure Theory

Interpolation and Approximation by Rational Functions in the Complex Domain

Interpolation and Approximation by Rational Functions in the Complex Domain

A Festschrift For Erich L. Lehmann

A Festschrift For Erich L. Lehmann

American Cobra Pilot

American Cobra Pilot

Inequalities in Mechanics and Physics

Inequalities in Mechanics and Physics

Groups and Representations

Groups and Representations

Applications of the Theory of Matrices

Applications of the Theory of Matrices

Classical Potential Theory and Its Probabilistic Counterpart

Classical Potential Theory and Its Probabilistic Counterpart

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