L P Harmonic Analysis On Sl 2 Mathbb R

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L P Harmonic Analysis On Sl 2 Mathbb R

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Author : William H. Barker
language : en
Publisher: American Mathematical Soc.
Release Date : 1988

L P Harmonic Analysis On Sl 2 Mathbb R written by William H. Barker 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 1988 with Mathematics categories.

The central result of this paper is a characterization of the image of [script]C[superscript italic]p([italic]G) under the operator-valued Fourier transform. The main thread through the paper is a careful analysis of the matrix coefficients for the discrete series and principal series of representations of [bold]SL (2, [bold]R). The paper is long, very technical and is not for the faint-hearted.

Foundations Of Time Frequency Analysis

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Author : Karlheinz Gröchenig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Foundations Of Time Frequency Analysis written by Karlheinz Gröchenig 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 2013-12-01 with Technology & Engineering categories.

Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.

Linear Canonical Transforms

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Author : John J. Healy
language : en
Publisher: Springer
Release Date : 2015-11-26

Linear Canonical Transforms written by John J. Healy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-26 with Science categories.

This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.

The Analytical Theory Of Heat

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Author : Jean-Baptiste-Joseph Fourier
language : en
Publisher:
Release Date : 1878

The Analytical Theory Of Heat written by Jean-Baptiste-Joseph Fourier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1878 with Heat categories.

Geometric Control Theory

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Author : Velimir Jurdjevic
language : en
Publisher: Cambridge University Press
Release Date : 1997

Geometric Control Theory written by Velimir Jurdjevic and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

Geometric control theory is concerned with the evolution of systems subject to physical laws but having some degree of freedom through which motion is to be controlled. This book describes the mathematical theory inspired by the irreversible nature of time evolving events. The first part of the book deals with the issue of being able to steer the system from any point of departure to any desired destination. The second part deals with optimal control, the question of finding the best possible course. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. The geometric language in which the results are expressed allows clear visual interpretations and makes the book accessible to physicists and engineers as well as to mathematicians.

Lectures On K3 Surfaces

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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2016-09-26

Lectures On K3 Surfaces written by Daniel Huybrechts and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-26 with Mathematics categories.

Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

Waves In Continuous Media

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Author : S. L. Gavrilyuk
language : en
Publisher: Springer
Release Date : 2017-01-27

Waves In Continuous Media written by S. L. Gavrilyuk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-27 with Mathematics categories.

Starting with the basic notions and facts of the mathematical theory of waves illustrated by numerous examples, exercises, and methods of solving typical problems Chapters 1 & 2 show e.g. how to recognize the hyperbolicity property, find characteristics, Riemann invariants and conservation laws for quasilinear systems of equations, construct and analyze solutions with weak or strong discontinuities, and how to investigate equations with dispersion and to construct travelling wave solutions for models reducible to nonlinear evolution equations. Chapter 3 deals with surface and internal waves in an incompressible fluid. The efficiency of mathematical methods is demonstrated on a hierarchy of approximate submodels generated from the Euler equations of homogeneous and non-homogeneous fluids. The self-contained presentations of the material is complemented by 200+ problems of different level of difficulty, numerous illustrations, and bibliographical recommendations.

Non Abelian Harmonic Analysis

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Author : Roger Howe
language : en
Publisher:
Release Date : 1992

Non Abelian Harmonic Analysis written by Roger Howe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

This book discusses the representation theory of the group SL(2, R), and some applications of this theory. The emphasis is in fact on the applications, some of which are outside representation theory and some are to representation theory itself. The topics outside representation theory are mostly of substantial classical importance (Fourier analysis, Laplace equation, Huyghen's Principle, Ergodic theory), while those inside representation theory mostly concern themes that have been central to Harish-Chandra's development of harmonic analysis on semisimple groups. This mix of topics should appeal to non-specialists in representation theory by illustrating how the theory can offer new perspectives on familiar topics, and by offering some insight into some important themes in representation theory itself.

Transmutation Operators And Applications

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Author : Vladislav V. Kravchenko
language : en
Publisher: Birkhäuser
Release Date : 2020-05-19

Transmutation Operators And Applications written by Vladislav V. Kravchenko and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-19 with Mathematics categories.

Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject.

Preference Learning

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Author : Johannes Fürnkranz
language : en
Publisher: Springer
Release Date : 2014-09-28

Preference Learning written by Johannes Fürnkranz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-28 with Computers categories.

The topic of preferences is a new branch of machine learning and data mining, and it has attracted considerable attention in artificial intelligence research in previous years. It involves learning from observations that reveal information about the preferences of an individual or a class of individuals. Representing and processing knowledge in terms of preferences is appealing as it allows one to specify desires in a declarative way, to combine qualitative and quantitative modes of reasoning, and to deal with inconsistencies and exceptions in a flexible manner. And, generalizing beyond training data, models thus learned may be used for preference prediction. This is the first book dedicated to this topic, and the treatment is comprehensive. The editors first offer a thorough introduction, including a systematic categorization according to learning task and learning technique, along with a unified notation. The first half of the book is organized into parts on label ranking, instance ranking, and object ranking; while the second half is organized into parts on applications of preference learning in multiattribute domains, information retrieval, and recommender systems. The book will be of interest to researchers and practitioners in artificial intelligence, in particular machine learning and data mining, and in fields such as multicriteria decision-making and operations research.