Author: Naum S. Landkof
Publisher: Springer
ISBN: 9783642651854
Category : Mathematics
Languages : en
Pages : 0
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Book Description
For a long time potential theory was necessarily viewed as only another chapter of mathematical physics. Developing in close connection with the theory of boundary-value problems for the Laplace operator, it led to the creation of the mathematical apparatus of potentials of single and double layers; this was adequate for treating problems involving smooth boundaries. A. M. Lyapunov is to be credited with the rigorous analysis of the properties of potentials and the possibilities for applying them to the 1 solution of boundary-value problems. The results he obtained at the end of the 19th century later received a more detailed and sharpened exposition in the book by N. M. Gunter, published in Paris in 1934 and 2 in New York 1967 with additions and revisions. Of fundamental significance to potential theory also was the work of H. Poincare, especially his method of sweeping out mass (balayage). At the beginning of the 20th century the work of S. Zaremba and especially of H. Lebesgue attracted the attention of mathematicians to the unsolvable cases of the classical Dirichlet problem. Through the efforts of O. Kellogg, G. Bouligand, and primarily N. Wiener, by the middle of the 20th century the problem of characterizing the so-called irregular points of the boundary of a region (i. e. the points at which the continuity of the solution of the Dirichlet problem may be violated) was completely solved and a procedure to obtain a generalized solution to the Dirichlet problem was described.
Author: Olav Kallenberg
Publisher: Springer Science & Business Media
ISBN: 9780387953137
Category : Mathematics
Languages : en
Pages : 670
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Book Description
The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.
Author: Oliver Dimon Kellogg
Publisher: Courier Corporation
ISBN: 9780486601441
Category : Science
Languages : en
Pages : 404
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Book Description
Introduction to fundamentals of potential functions covers the force of gravity, fields of force, potentials, harmonic functions, electric images and Green's function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential, and much more. Detailed proofs rigorously worked out. 1929 edition.
Author: Kurt Mahler
Publisher: CUP Archive
ISBN:
Category : Mathematics
Languages : en
Pages : 114
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Book Description
Author: K. GowriSankaran
Publisher: Springer Science & Business Media
ISBN: 9401111383
Category : Mathematics
Languages : en
Pages : 467
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Book Description
Proceedings of the NATO Advanced Research Workshop, Château de Bonas, France, July 25--31, 1993
Author: Olav Kallenberg
Publisher: Springer Nature
ISBN: 3030618714
Category : Mathematics
Languages : en
Pages : 931
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Book Description
The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.
Author: Steven Weinberg
Publisher: Cambridge University Press
ISBN: 1108841767
Category : Science
Languages : en
Pages : 325
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Book Description
Nobel Laureate Steven Weinberg explains the foundations of modern physics in historical context for undergraduates and beyond.
Author: Hiroaki Aikawa
Publisher: Springer
ISBN: 3540699910
Category : Mathematics
Languages : en
Pages : 208
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Book Description
The first part of these lecture notes is an introduction to potential theory to prepare the reader for later parts, which can be used as the basis for a series of advanced lectures/seminars on potential theory/harmonic analysis. Topics covered in the book include minimal thinness, quasiadditivity of capacity, applications of singular integrals to potential theory, L(p)-capacity theory, fine limits of the Nagel-Stein boundary limit theorem and integrability of superharmonic functions. The notes are written for an audience familiar with the theory of integration, distributions and basic functional analysis.
Author: Jerry Tobias
Publisher: Elsevier
ISBN: 0323148581
Category : Science
Languages : en
Pages : 485
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Book Description
Foundations of Modern Auditory Theory, Volume I is an 11-chapter text that covers the basic auditory processes. This volume deals first with the electrophysiological and conditioning data that reflect periodicity perception, the analysis of high-frequency tones, and the mechanisms and effects of auditory masking. These topics are followed by discussions on the poststimulatory auditory fatigue and adaptation; the theoretical bases necessary for an understanding of the critical band's ubiquity; and the mechanical events in transformation process occurring in cochlea. This volume describes the anatomical structure and electrophysiological action of the cochlea and further explores ear models to study the mechanical properties of the auditory system and the basic neural transmission processes and their properties. The concluding chapters look into the distinct patterns of disorder in psychoacoustic function and the perception of musical stimuli. This book is an ideal source for teachers and students who wish to understand the mechanisms of the auditory system.
Author: C. van den Berg
Publisher: Springer
ISBN: 3540391835
Category : Mathematics
Languages : en
Pages : 331
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Book Description
