Problems And Solutions In Banach Spaces Hilbert Spaces Fourier Transform Wavelets Generalized Functions And Quantum Mechanics

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Problems And Solutions In Banach Spaces Hilbert Spaces Fourier Transform Wavelets Generalized Functions And Quantum Mechanics

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Author : Willi-hans Steeb
language : en
Publisher: World Scientific
Release Date : 2022-08-23

Problems And Solutions In Banach Spaces Hilbert Spaces Fourier Transform Wavelets Generalized Functions And Quantum Mechanics written by Willi-hans Steeb and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-23 with Mathematics categories.

This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions.The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included.

Problems And Solutions In Banach Spaces Hilbert Spaces Fourier Transform Wavelets Generalized Functions And Quantum Mechanics

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Author : WILLI-HANS. MATHIS STEEB (WOLFGANG.)
language : en
Publisher: World Scientific Publishing Company
Release Date : 2022-09-24

Problems And Solutions In Banach Spaces Hilbert Spaces Fourier Transform Wavelets Generalized Functions And Quantum Mechanics written by WILLI-HANS. MATHIS STEEB (WOLFGANG.) and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-24 with Mathematics categories.

This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions.The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2003

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

Hilbert Spaces Wavelets Generalised Functions And Modern Quantum Mechanics

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Author : W.-H. Steeb
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-09-30

Hilbert Spaces Wavelets Generalised Functions And Modern Quantum Mechanics written by W.-H. Steeb and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-30 with Science categories.

This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics. The book is suitable for graduate students in physics and mathematics.

Hilbert Spaces Generalized Functions And Quantum Mechanics

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Author : Willi-Hans Steeb
language : en
Publisher:
Release Date : 1991

Hilbert Spaces Generalized Functions And Quantum Mechanics written by Willi-Hans Steeb and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Hilbert space categories.

Quaternionic Hilbert Spaces And Slice Hyperholomorphic Functions

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Author : Daniel Alpay
language : en
Publisher: Springer Nature
Release Date : 2024-12-09

Quaternionic Hilbert Spaces And Slice Hyperholomorphic Functions written by Daniel Alpay and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-09 with Mathematics categories.

The purpose of the present book is to develop the counterparts of Banach and Hilbert spaces in the setting of slice hyperholomorphic functions. Banach and Hilbert spaces of analytic functions, in one or several complex variables, play an important role in analysis and related fields. Besides their intrinsic interest, such spaces have numerous applications. The book is divided into three parts. In the first part, some foundational material on quaternionic functions and functional analysis are introduced. The second part is the core of the book and contains various types of functions spaces ranging from the Hardy spaces, also in the fractional case, to the Fock space extended to the case of quaternions. The third and final part present some further generalization. Researchers in functional analysis and hypercomplex analysis will find this book a key contribution to their field, but also researchers in mathematical physics, especially in quantum mechanics, will benefit from the insights presented.

Denseness Bases And Frames In Banach Spaces And Applications

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Author : Aref Jeribi
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-03-19

Denseness Bases And Frames In Banach Spaces And Applications written by Aref Jeribi and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-19 with Mathematics categories.

This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. Contents Introduction Linear operators Basic notations and results Bases Semi-groups Discrete operator and denseness of the generalized eigenvectors Frames in Hilbert spaces Summability of series ν-convergence operators Γ-hypercyclic set of linear operators Analytic operators in Béla Szökefalvi-Nagy’s sense Bases of the perturbed operator T(ε) Frame of the perturbed operator T(ε) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory

Analysis In Banach Spaces

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Author : Tuomas Hytönen
language : en
Publisher: Springer
Release Date : 2016-11-26

Analysis In Banach Spaces written by Tuomas Hytönen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-26 with Mathematics categories.

The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas.

Noncommutative Geometry Quantum Fields And Motives

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Author : Alain Connes
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-03-13

Noncommutative Geometry Quantum Fields And Motives written by Alain Connes and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-13 with Mathematics categories.

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.

Banach And Hilbert Spaces Of Vector Valued Functions

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Author : Jacob Burbea
language : en
Publisher: Pitman Publishing
Release Date : 1984

Banach And Hilbert Spaces Of Vector Valued Functions written by Jacob Burbea and has been published by Pitman Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Banach spaces categories.