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A Panaroma of Harmonic Analysis

Author: Steven G Krantz
Publisher: Cambridge : Cambridge University Press, 2014.
Series: Carus.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Krantz, Steven G.
Panaroma of Harmonic Analysis.
Washington : Mathematical Association of America, ©2014
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Steven G Krantz
ISBN: 9781614440260 1614440263
OCLC Number: 889964970
Notes: Title from publishers bibliographic system (viewed on 09 Jun 2014).
Description: 1 online resource.
Contents: ""Front cover ""; ""copyright page ""; ""title page ""; ""Preface""; ""0 Overview of Measure Theory and Functional Analysis""; ""0.1 Pre-Basics""; ""0.2 A Whirlwind Review of Measure Theory""; ""0.3 The Elements of Banach Space Theory""; ""0.4 Hilbert Space""; ""0.5 Two Fundamental Principles ofFunctional Analysis""; ""1 Fourier Series Basics""; ""1.0 The Pre-History of Fourier Analysis""; ""1.1 The Rudiments of Fourier Series""; ""1.2 Summability of Fourier Series""; ""1.3 A Quick Introduction toSummability Methods""; ""1.4 Key Properties of Summability Kernels"" ""1.5 Pointwise Convergence for Fourier Series""""1.6 Norm Convergence of Partial Sums andthe Hilbert Transform""; ""2 The Fourier Transform""; ""2.1 Basic Properties of the Fourier Transform""; ""2.2 Invariance and Symmetry Properties ofthe Fourier Transform""; ""2.3 Convolution and Fourier Inversion""; ""2.4 The Uncertainty Principle""; ""3 Multiple Fourier Series""; ""3.1 Various Methods of Partial Summation""; ""3.2 Examples of Different Typesof Summation""; ""3.3 Fourier Multipliers and the Summation of Series"" ""3.4 Applications of the Fourier MultiplierTheorems to Summation of MultipleTrigonometric Series""""3.5 The Multiplier Problem for the Ball""; ""4 Spherical Harmonics""; ""4.1 A New Look at Fourier Analysis in the Plane""; ""4.2 Further Results on Spherical Harmonics""; ""5 Fractional Integrals, Singular Integrals, and Hardy Spaces""; ""5.1 Fractional Integrals and Other Elementary Operators""; ""5.2 Prolegomena to Singular Integral Theory""; ""5.3 An Aside on Integral Operators""; ""5.4 A Look at Hardy Spaces in the Complex Plane""; ""5.5 The Real-Variable Theory of Hardy Spaces"" ""5.6 The Maximal-Function Characterization of Hardy Spaces""""5.7 The Atomic Theory of Hardy Spaces""; ""5.8 Ode to BMO""; ""6 Modern Theories of Integral Operators""; ""6.1 Spaces of Homogeneous Type""; ""6.2 Integral Operators on a Space of Homogeneous Type""; ""6.3 A New Look at Hardy Spaces""; ""6.4 The T(1) Theorem""; ""7 Wavelets""; ""7.1 Localization in the Timeand Space Variables""; ""7.2 Building a Custom Fourier Analysis""; ""7.3 The Haar Basis""; ""7.4 Some Illustrative Examples""; ""7.5 Construction of a Wavelet Basis""; ""8 A Retrospective"" ""8.1 Fourier Analysis: An Historical Overview""""Appendices and Ancillary Material""; ""I The Existence of Testing Functions andTheir Density in L^p""; ""II Schwartz Functions and the Fourier Transform""; ""III The Interpolation Theorems of Marcinkiewicz and Riesz-Thorin""; ""IV Hausdorff Measure and Surface Measure""; ""V Green�s Theorem""; ""VI The Banach-Alaoglu Theorem""; ""VII Expressing an Integral in Terms of the Distribution Function""; ""VIII The Stone-Weierstrass Theorem""; ""IX Landau�s O and o Notation""; ""Table of Notation""; ""Bibliography""; ""Index""
Series Title: Carus.
Responsibility: Steven G. Krantz.

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