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Author: Béla Sz Nagy Publisher: Springer Science & Business Media ISBN: 1441960937 Category : Mathematics Languages : en Pages : 481
Book Description
The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
Author: Béla Sz Nagy Publisher: Springer Science & Business Media ISBN: 1441960937 Category : Mathematics Languages : en Pages : 481
Book Description
The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
Author: I. M. Gel'fand Publisher: Academic Press ISBN: 1483262243 Category : Mathematics Languages : en Pages : 399
Book Description
Generalized Functions, Volume 4: Applications of Harmonic Analysis is devoted to two general topics—developments in the theory of linear topological spaces and construction of harmonic analysis in n-dimensional Euclidean and infinite-dimensional spaces. This volume specifically discusses the bilinear functionals on countably normed spaces, Hilbert-Schmidt operators, and spectral analysis of operators in rigged Hilbert spaces. The general form of positive generalized functions on the space S, continuous positive-definite functions, and conditionally positive generalized functions are also deliberated. This publication likewise considers the mean of a generalized random process, multidimensional generalized random fields, simplest properties of cylinder sets, and definition of Gaussian measures. This book is beneficial to students, specialists, and researchers aiming to acquire knowledge of functional analysis.
Author: Mischa Cotlar Publisher: American Mathematical Soc. ISBN: 9780821855263 Category : Mathematics Languages : en Pages : 532
Book Description
This book is a collection of papers reflecting the conference held in Caracas, Venezuela, in January 1994 in celebration of Professor Mischa Cotlar's eightieth birthday. Presenting an excellent account of recent advances in harmonic analysis and operator theory and their applications, many of the contributors are world leaders in their fields. The collection covers a broad spectrum of topics, including: wavelet analysis, Haenkel operators, multimeasure theory, the boundary behavior of the Bergman kernel, interpolation theory, and Cotlar's Lemma on almost orthogonality in the context of L[superscript p] spaces and more... The range of topics in this volume promotes cross-pollination among the various fields covered. Such variety makes "Harmonic Analysis and Operator Theory" an inspiration for graduate students interested in this area of study.
Author: Maurice A. de Gosson Publisher: Springer Science & Business Media ISBN: 3764399929 Category : Mathematics Languages : en Pages : 351
Book Description
The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.
Author: Béla Sz Nagy
Author: Béla Sz Nagy
Author: B. La Sz -Nagy
Author: Leonard Gross
Author: B. Sz.-nagy
Author: Béla Szőkefalvi-Nagy
Author: Béla Szőkefalvi-Nagy
Author: I. M. Gel'fand
Author: Béla Szőkefalvi-Nagy
Author: Mischa Cotlar
Author: Maurice A. de Gosson