Muutke küpsiste eelistusi

E-raamat: Harmonic Analysis on the Real Line: A Path in the Theory

  • Formaat: EPUB+DRM
  • Sari: Pathways in Mathematics
  • Ilmumisaeg: 27-Sep-2021
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030818920
Teised raamatud teemal:
  • Formaat - EPUB+DRM
  • Hind: 55,56 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Harmonic Analysis on the Real Line: A Path in the TheorySuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Pathways in Mathematics
  • Ilmumisaeg: 27-Sep-2021
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030818920
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

This book sketches a path for newcomers into the theory of harmonic analysis on the real line. It presents a collection of both basic, well-known and some less known results that may serve as a background for future research around this topic. Many of these results are also a necessary basis for multivariate extensions. An extensive bibliography, as well as hints to open problems are included. The book can be used as a skeleton for designing certain special courses, but it is also suitable for self-study.

Arvustused

The book under review takes the reader on a journey along a particular path through the vast landscape of modern harmonic analysis in one real variable. From beginning to end, the text is uniquely flavored by the authors mathematical interests which provides the reader with a good sense of direction. The book should be accessible to beginning graduate students in analysis and advanced undergraduates with basic knowledge in real analysis . (Joris Roos, zbMATH 1514.42001, 2023) This book is very accurately described by its subtitle a path in the theory. The book is at times a textbook, an introduction to harmonic analysis, an essay, or a survey, or some combination of these. Some theorems are stated and proved, some are discussed, and others are quickly mentioned. It's not a standard path, but an engaging one, offering insights and connections that arenew or not well known. (Charles N. Moore, Mathematical Reviews, September, 2022)

1 Introduction
1.1 Motivation and Background
1(1)
1.2 Structure
2(1)
1.3 Before Reading the Book
3(2)
2 Classes of Functions
5(18)
2.1 Continuous Functions and Lebesgue Spaces
5(10)
2.1.1 Continuous Functions
5(2)
2.1.2 Lebesgue Spaces
7(4)
2.1.3 The Hardy--Littlewood Maximal Function
11(1)
2.1.4 Calderon--Zygmund Decomposition
12(2)
2.1.5 Absolute Continuity
14(1)
2.2 Functions of Bounded Variation
15(8)
3 Fourier Series
23(24)
3.1 Definition and Basic Properties
23(4)
3.2 Convergence
27(6)
3.3 Absolute Convergence
33(3)
3.4 Lebesgue Constants
36(3)
3.5 Summability
39(2)
3.6 Trigonometric Series Versus Fourier Series
41(6)
4 Fourier Transform
47(24)
4.1 Definitions and Around
47(7)
4.2 From Discussion to Calculations
54(3)
4.3 Poisson Summation Formula
57(2)
4.4 Amalgam Type Spaces
59(2)
4.5 Summability
61(10)
4.5.1 Summability and Poisson Summation
63(2)
4.5.2 Wiener Algebras and Bounded Variation
65(6)
5 Hilbert Transform
71(30)
5.1 Definitions and Calculations
72(2)
5.2 The Hilbert Transform Comes into Play
74(3)
5.3 Existence Almost Everywhere
77(4)
5.3.1 Weak Estimate
77(3)
5.3.2 Extension to L1
80(1)
5.4 Integrabiliry of the Hilbert Transform
81(3)
5.5 Special Cases of the Hilbert Transform
84(10)
5.5.1 Conditions for the Integrability of the Hilbert Transform
88(3)
5.5.2 General Conditions
91(3)
5.6 Summability to the Hilbert Transform
94(7)
6 Hardy Spaces and their Subspaces
101(30)
6.1 Some Starting Points
102(1)
6.2 Atomic Characterization
103(6)
6.2.1 Atoms
103(2)
6.2.2 Atomic Proof of the Fourier--Hardy Inequality
105(1)
6.2.3 A Postponed Proof
106(2)
6.2.4 More About Atomic Characterization
108(1)
6.3 Molecular Characterization
109(4)
6.4 Subspaces
113(5)
6.5 A Paley--Wiener Theorem
118(2)
6.6 Discrete Hardy Spaces
120(5)
6.7 Back to Trigonometric Series
125(6)
7 Hardy Inequalities
131(10)
7.1 Discrete Hardy Inequality
133(2)
7.2 Hardy Inequalities for Hausdorff Operators
135(6)
8 Certain Applications
141(42)
8.1 Interpolation Properties of a Scale of Spaces
141(10)
8.1.1 Results
143(1)
8.1.2 Proofs
144(7)
8.2 Fourier Re-expansions
151(6)
8.3 Absolute Convergence
157(6)
8.3.1 Proof of the Main Theorem
159(3)
8.3.2 Proof of the Corollary
162(1)
8.3.3 Proof of the Extended Theorem
162(1)
8.4 Boas' Conjecture
163(5)
8.5 Salem Type Conditions
168(4)
8.5.1 Non-periodic Salem Conditions
169(1)
8.5.2 Applications
170(2)
8.6 L1 Convergence of Fourier Transforms
172(8)
8.6.1 L1 Convergence
175(3)
8.6.2 Application to Trigonometric Series
178(2)
8.7 More About Applications
180(3)
Basic Notations 183(4)
Bibliography 187(8)
Index 195
Elijah Liflyand has recently retired from his position at the Department of Mathematics at Bar-Ilan University in Israel, but not from mathematics. He also holds a position at the at the Regional Mathematical Center of Southern Federal University in Rostov-on-Don, Russia. His areas of expertise are in Fourier Analysis, Complex Analysis, and Approximation Theory, among others. With Birkhäuser/Springer, he has published two books: "Decay of the Fourier Transform" (with Alex Iosevich, 2014), and "Functions of Bounded Variation and Their Fourier Transforms" (in the Applied Numerical and Harmonic Analysis series, 2019).
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97830308189206e.html
Märksõnad: