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Essential Results of Functional Analysis

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Essential Results of Functional Analysis (Chicago Lectures in Mathematics) by Robert J. Zimmer
English | 1990-01-15 | ISBN: 0226983382 | 168 pages | PDF | 3,7 MB

Essential Results of Functional Analysis
Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis.

It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach.

Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed by a discussion of various examples of topological vector spaces, seminorms defining them, and natural classes of linear operators. He then presents basic results for a wide range of topics: convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. In treating all of these topics, Zimmer's emphasis is not on the development of all related machinery or on encyclopedic coverage but rather on the direct, complete presentation of central theorems and the structural framework and examples needed to understand them. Sets of exercises are included at the end of each chapter.

For graduate students and researchers in mathematics who have mastered elementary analysis, this book is an entrée and reference to the full range of theory and applications in which functional analysis plays a part. For physics students and researchers interested in these topics, the lectures supply a thorough mathematical grounding.
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Essential Results of Functional Analysis

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Essential Results of Functional Analysis (Chicago Lectures in Mathematics) by Robert J. Zimmer
English | 1990-01-15 | ISBN: 0226983382 | 168 pages | PDF | 3,7 MB

Essential Results of Functional Analysis
Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis.

It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach.

Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed by a discussion of various examples of topological vector spaces, seminorms defining them, and natural classes of linear operators. He then presents basic results for a wide range of topics: convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. In treating all of these topics, Zimmer's emphasis is not on the development of all related machinery or on encyclopedic coverage but rather on the direct, complete presentation of central theorems and the structural framework and examples needed to understand them. Sets of exercises are included at the end of each chapter.

For graduate students and researchers in mathematics who have mastered elementary analysis, this book is an entrée and reference to the full range of theory and applications in which functional analysis plays a part. For physics students and researchers interested in these topics, the lectures supply a thorough mathematical grounding.
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Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere…

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Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball by Volker Michel
English | 2012-12-11 | ISBN: 0817684026 | PDF | 342 pages | 6 MB

Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere…
Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author's lectures on classical approximation methods based on orthogonal polynomials and selected tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth's or the brain's interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.
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A User’s Guide to Measure Theoretic Probability

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A User's Guide to Measure Theoretic Probability By David Pollard
2001 | 366 Pages | ISBN: 0521002893 , 0521802423 | PDF | 39 MB

A User’s Guide to Measure Theoretic Probability
Rigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This 2002 book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.
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Handbook of Real-Time Fast Fourier Transforms: Algorithms to Product Testing

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Handbook of Real-Time Fast Fourier Transforms: Algorithms to Product Testing
by Winthrop W. Smith, Joanne M. Smith
English | 1995 | ISBN: 0780310918 | 468 pages | PDF | 51.89 MB

Handbook of Real-Time Fast Fourier Transforms: Algorithms to Product Testing
""This useful, logical, unbiased, FFT compendium allows the user to quickly and accurately obtain practical information to implement a solution or simply acquire a general overview without spending months gathering this information elsewhere."
-Jay Perry, Executive Vice President, Technology, Catalina Research, Inc.

"This is a practical guide for understanding and using FFTs. Win's (Winthrop Smith, author) years of experience using FFTs to solve real-world problems comes through on page after page. If you're building an FFT processor, you'll find this book indispensable."
-Tony Agnello, President, Ariel Corp.

FFTs are at the heart of ADSL, the new telecom standard (T1.413), which allows phones to transfer digital data 200 times faster and simultaneously transmit speech. Fast Fourier Transforms (FFTs) synthesize, recognize, enhance, compress, modify, or analyze signals in products such as Doppler weather radar, CT and MRI scans, AWACS radar, and satellite imaging radar. In this book, you will get the foundation and facts you need to implement FFT algorithms for many diverse applications. Key features you will put to immediate use include:
– Comparison matrices and performance measures for objective selection of weighting functions, algorithm building blocks, algorithms, algorithm mappings, arithmetic formats, and DSP chips
– Extensive algorithm examples with instructions for memory mapping and conversion to code
– An unbiased listing of the FFT features of 51 fixed-point DSP chips, including ASIC and multiprocessor chips, 13 floating-point DSP chips, and six dedicated FFT chips
– Test signals with instructions and examples on how to detect and isolate errors during: FFT algorithm/code development and debugging, and end-product operation
– Design examples for products that use frequency analysis, power spectrum estimation, linear filtering, and two-dimensional processing
– Questions and answers for selecting commercial-off-the-shelf DSP boards

An all-in-one-source for implementing real-time FFT algorithms of any length, this book will be essential to engineers and other technical innovators who want to stay on the cutting edge of FFT technology."
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Handbook of Real-Time Fast Fourier Transforms: Algorithms to Product Testing

FREEDownload : Handbook of Real-Time Fast Fourier Transforms: Algorithms to Product Testing

Handbook of Real-Time Fast Fourier Transforms: Algorithms to Product Testing
by Winthrop W. Smith, Joanne M. Smith
English | 1995 | ISBN: 0780310918 | 468 pages | PDF | 51.89 MB

Handbook of Real-Time Fast Fourier Transforms: Algorithms to Product Testing
""This useful, logical, unbiased, FFT compendium allows the user to quickly and accurately obtain practical information to implement a solution or simply acquire a general overview without spending months gathering this information elsewhere."
-Jay Perry, Executive Vice President, Technology, Catalina Research, Inc.

"This is a practical guide for understanding and using FFTs. Win's (Winthrop Smith, author) years of experience using FFTs to solve real-world problems comes through on page after page. If you're building an FFT processor, you'll find this book indispensable."
-Tony Agnello, President, Ariel Corp.

FFTs are at the heart of ADSL, the new telecom standard (T1.413), which allows phones to transfer digital data 200 times faster and simultaneously transmit speech. Fast Fourier Transforms (FFTs) synthesize, recognize, enhance, compress, modify, or analyze signals in products such as Doppler weather radar, CT and MRI scans, AWACS radar, and satellite imaging radar. In this book, you will get the foundation and facts you need to implement FFT algorithms for many diverse applications. Key features you will put to immediate use include:
– Comparison matrices and performance measures for objective selection of weighting functions, algorithm building blocks, algorithms, algorithm mappings, arithmetic formats, and DSP chips
– Extensive algorithm examples with instructions for memory mapping and conversion to code
– An unbiased listing of the FFT features of 51 fixed-point DSP chips, including ASIC and multiprocessor chips, 13 floating-point DSP chips, and six dedicated FFT chips
– Test signals with instructions and examples on how to detect and isolate errors during: FFT algorithm/code development and debugging, and end-product operation
– Design examples for products that use frequency analysis, power spectrum estimation, linear filtering, and two-dimensional processing
– Questions and answers for selecting commercial-off-the-shelf DSP boards

An all-in-one-source for implementing real-time FFT algorithms of any length, this book will be essential to engineers and other technical innovators who want to stay on the cutting edge of FFT technology."
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Excursions in Harmonic Analysis, Volume 1: The February Fourier Talks at the Norbert Wiener Center

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Excursions in Harmonic Analysis, Volume 1: The February Fourier Talks at the Norbert Wiener Center by Travis D Andrews and Radu Balan
English | 2013 | ISBN: 0817683755 | PDF | 506 pages | 7 MB

Excursions in Harmonic Analysis, Volume 1: The February Fourier Talks at the Norbert Wiener Center
The Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis. This two-volume set consists of contributions from speakers at the February Fourier Talks (FFT) from 2006-2011. The FFT are organized by the Norbert Wiener Center in the Department of Mathematics at the University of Maryland, College Park. These volumes span a large spectrum of harmonic analysis and its applications. They are divided into the following parts: Volume I • Sampling Theory • Remote Sensing • Mathematics of Data Processing • Applications of Data Processing Volume II • Measure Theory • Filtering • Operator Theory • Biomathematics Each part provides state-of-the-art results, with contributions from an impressive array of mathematicians, engineers, and scientists in academia, industry, and government. Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center is an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.
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Principles of Partial Differential Equations

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Principles of Partial Differential Equations (Problem Books in Mathematics) by Alexander Komech and Andrew Komech
English | 2009 | ISBN: 1441910956 | 161 pages | PDF | 1 MB
This concise book covers the classical tools of PDE theory used in today's science and engineering: characteristics, the wave propagation, the Fourier method, distributions, Sobolev spaces, fundamental solutions, and Green's functions.

Principles of Partial Differential Equations
The approach is problem-oriented, giving the reader an opportunity to master solution techniques. The theoretical part is rigorous and with important details presented with care. Hints are provided to help the reader restore the arguments to their full rigor. Many examples from physics are intended to keep the book intuitive and to illustrate the applied nature of the subject. The book is useful for a higher-level undergraduate course and for self-study.
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An Introduction to Stein’s Method

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A. D. Barbour, Louis H. Y. Chen, "An Introduction to Stein's Method"
2005 | ISBN-10: 981256280X, 8175961368 | 240 pages | PDF | 8 MB

An Introduction to Stein’s Method
A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems. This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.
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