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Fourier Series Notes


 - Pointwise Convergence of Fourier Series (Lecture Notes in Mathematics)
Pointwise Convergence of Fourier Series (Lecture Notes in Mathematics)

This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.

  • Brand: Brand: Springer
  • ASIN: 3540432701
 - Differential Equations with Applications and Historical Notes (Textbooks in Mathematics)
Differential Equations with Applications and Historical Notes (Textbooks in Mathematics)

Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the achievements of one’s own time. An unfortunate effect of the predominance of fads is that if a student doesn’t learn about such worthwhile topics as the wave equation, Gauss’s hypergeometric function, the gamma function, and the basic problems of the calculus of variations—among others—as an undergraduate, then he/she is unlikely to do so later. The natural place for an informal acquaintance with such ideas is a leisurely introductory course on differential equations. Specially designed for just such a course, Differential Equations with Applications and Historical Notes takes great pleasure in the journey into the world of differential equations and their wide range of applications. The author—a highly respected educator—advocates a careful approach, using explicit explanation to ensure students fully comprehend the subject matter.With an emphasis on modeling and applications, the long-awaited Third Edition of this classic textbook presents a substantial new section on Gauss’s bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activ...

  • ASIN: B01N767H4I
 - Differential Equations with Applications and Historical Notes, 2nd Edition (International Series in Pure and Applied Mathematics)
Differential Equations with Applications and Historical Notes, 2nd Edition (International Series in Pure and Applied Mathematics)

A revision of a much-admired text distinguished by the exceptional prose and historical/mathematical context that have made Simmons' books classics. The Second Edition includes expanded coverage of Laplace transforms and partial differential equations as well as a new chapter on numerical methods.

  • ASIN: 0070575401
 - Computational Methods in Finance (Chapman and Hall/CRC Financial Mathematics Series)
Computational Methods in Finance (Chapman and Hall/CRC Financial Mathematics Series)

As today’s financial products have become more complex, quantitative analysts, financial engineers, and others in the financial industry now require robust techniques for numerical analysis. Covering advanced quantitative techniques, Computational Methods in Finance explains how to solve complex functional equations through numerical methods. The first part of the book describes pricing methods for numerous derivatives under a variety of models. The book reviews common processes for modeling assets in different markets. It then examines many computational approaches for pricing derivatives. These include transform techniques, such as the fast Fourier transform, the fractional fast Fourier transform, the Fourier-cosine method, and saddlepoint method; the finite difference method for solving PDEs in the diffusion framework and PIDEs in the pure jump framework; and Monte Carlo simulation. The next part focuses on essential steps in real-world derivative pricing. The author discusses how to calibrate model parameters so that model prices are compatible with market prices. He also covers various filtering techniques and their implementations and gives examples of filtering and parameter estimation. Developed from the author’s courses at Columbia University and the Courant Ins...

  • Brand: Brand: CRC Press
  • ASIN: 1439829578
 - Principles of Musical Acoustics (Undergraduate Lecture Notes in Physics)
Principles of Musical Acoustics (Undergraduate Lecture Notes in Physics)

Principles of Musical Acoustics focuses on the basic principles in the science and technology of music. Musical examples and specific musical instruments demonstrate the principles. The book begins with a study of vibrations and waves, in that order. These topics constitute the basic physical properties of sound, one of two pillars supporting the science of musical acoustics. The second pillar is the human element, the physiological and psychological aspects of acoustical science. The perceptual topics include loudness, pitch, tone color, and localization of sound. With these two pillars in place, it is possible to go in a variety of directions. The book treats in turn, the topics of room acoustics, audio both analog and digital, broadcasting, and speech. It ends with chapters on the traditional musical instruments, organized by family. The mathematical level of this book assumes that the reader is familiar with elementary algebra. Trigonometric functions, logarithms and powers also appear in the book, but computational techniques are included as these concepts are introduced, and there is further technical help in appendices.

  • ASIN: B00E5U5JAW
 - Lectures on Bochner-Riesz Means (London Mathematical Society Lecture Note Series Book 114)
Lectures on Bochner-Riesz Means (London Mathematical Society Lecture Note Series Book 114)

This book is concerned with the modern theory of Fourier series. Treating developments since Zygmund's classic study, the authors begin with a thorough discussion of the classical one-dimensional theory from a modern perspective. The text then takes up the developments of the 1970s, beginning with Fefferman's famous disc counterexample. The culminating chapter presents Cordoba's geometric theory of Kayeka maximal functions and multipliers. Research workers in the fields of Fourier analysis and harmonic analysis will find this a valuable account of these developments. Second year graduate students, who are familiar with Lebesgue theory and are acquainted with distributions, will be able to use this as a textbook which will bring them up to the exciting open questions in the field.

  • ASIN: B01DM2B5J2
 - Descriptive Set Theory and the Structure of Sets of Uniqueness (London Mathematical Society Lecture Note Series Book 128)
Descriptive Set Theory and the Structure of Sets of Uniqueness (London Mathematical Society Lecture Note Series Book 128)

The study of sets of uniqueness for trigonometric series has a long history, originating in the work of Riemann, Heine, and Cantor in the mid-nineteenth century. Since then it has been a fertile ground for numerous investigations involving real analysis, classical and abstract harmonic analysis, measure theory, functional analysis and number theory. In this book are developed the intriguing and surprising connections that the subject has with descriptive set theory. These have only been discovered recently and the authors present here this novel theory which leads to many new results concerning the structure of sets of uniqueness and include solutions to some of the classical problems in this area. In order to make the material accessible to logicians, set theorists and analysts, the authors have covered in some detail large parts of the classical and modern theory of sets of uniqueness as well as the relevant parts of descriptive set theory. Thus the book is essentially self-contained and will make an excellent introduction to the subject for graduate students and research workers in set theory and analysis.

  • ASIN: B01DM2AV92
 - Harmonic Analysis and Integral Geometry (Chapman & Hall/CRC Research Notes in Mathematics Series)
Harmonic Analysis and Integral Geometry (Chapman & Hall/CRC Research Notes in Mathematics Series)

Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lecture

  • ASIN: B00SC8G3BW
 - Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics)
Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics)

The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

  • Brand: imusti
  • ASIN: 007054235X
 - Shentesel Bicycle Front Fork Speed Lock Cap Cover Bike Part for SR Suntour XCT XCM XCR - XCT
Shentesel Bicycle Front Fork Speed Lock Cap Cover Bike Part for SR Suntour XCT XCM XCR - XCT

Item Name: Bike Lock Cap Cover Material: Plastic Features: Lightweight, Portable, Easy to Use, Bike Accessories Notes: For XCR and for Epicon are universal. Due to the light and screen setting difference, the item's color may be slightly different from the pictures. Package Includes: 1 x Bike Lock Cap Cover

  • Color: XCT
  • Brand: Shentesel
  • ASIN: B07S3GCVFL

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