A Panaroma of Harmonic Analysis

Steven G. Krantz

doi:10.5948/UPO9781614440260

This book is no longer available to purchase from Cambridge Core
Cited by 20
Cited by
- 20
Crossref Citations

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Ashino, Ryuichi and Mandai, Takeshi 2003. Wavelet Bases for Microlocal Filtering and the Sampling Theorem inLp(Rn)∗. Applicable Analysis, Vol. 82, Issue. 1, p. 1.

CrossRef

Google Scholar

Krantz, Steven G. 2008. A tale of three kernels. Complex Variables and Elliptic Equations, Vol. 53, Issue. 11, p. 1059.

CrossRef

Google Scholar

Krantz, Steven G. 2008. The Hartogs extension phenomenon redux. Complex Variables and Elliptic Equations, Vol. 53, Issue. 4, p. 343.

CrossRef

Google Scholar

Gunzburger, Max Lee, Eunjung Saka, Yuki Trenchea, Catalin and Wang, Xiaoming 2010. Analysis of Nonlinear Spectral Eddy-Viscosity Models of Turbulence. Journal of Scientific Computing, Vol. 45, Issue. 1-3, p. 294.

CrossRef

Google Scholar

Alan C. Lazer and Mark Leckband 2010. The Fundamental Theorem of Algebra via the Fourier Inversion Formula. The American Mathematical Monthly, Vol. 117, Issue. 5, p. 455.

CrossRef

Google Scholar

Ortner, Norbert 2011. The Fourier exchange theorem for kernels. Applicable Analysis, Vol. 90, Issue. 11, p. 1635.

CrossRef

Google Scholar

2011. The Integral: A Crux for Analysis.

CrossRef

Google Scholar

Krantz, Steven G. 2011. Harmonic analysis. WIREs Computational Statistics, Vol. 3, Issue. 2, p. 163.

CrossRef

Google Scholar

Chakrabarty, Arijit Hazra, Rajat Subhra and Sarkar, Deepayan 2016. From random matrices to long range dependence. Random Matrices: Theory and Applications, Vol. 05, Issue. 02, p. 1650008.

CrossRef

Google Scholar

Tendero, Yohann and Morel, Jean-Michel 2016. On the Mathematical Foundations of Computational Photography. Journal of Mathematical Imaging and Vision, Vol. 54, Issue. 3, p. 378.

CrossRef

Google Scholar

Krantz, Steven G. 2017. Harmonic and Complex Analysis in Several Variables. p. 59.

CrossRef

Google Scholar

Krantz, Steven G. 2017. Harmonic and Complex Analysis in Several Variables. p. 395.

CrossRef

Google Scholar

Krantz, Steven G. 2017. Harmonic and Complex Analysis in Several Variables. p. 1.

CrossRef

Google Scholar

Anderson, Theresa C. Hytönen, Tuomas and Tapiola, Olli 2017. Weak $$A_\infty $$ Weights and Weak Reverse Hölder Property in a Space of Homogeneous Type. The Journal of Geometric Analysis, Vol. 27, Issue. 1, p. 95.

CrossRef

Google Scholar

Krantz, Steven G. 2017. Harmonic and Complex Analysis in Several Variables. p. 89.

CrossRef

Google Scholar

Zhao, Dongxiao and Aluie, Hussein 2018. Inviscid criterion for decomposing scales. Physical Review Fluids, Vol. 3, Issue. 5,

CrossRef

Google Scholar

Orenstein, Adam 2018. Fredholm Operators in the Toeplitz Algebra $${\mathcal {I}}(QC)$$ I ( Q C ). Complex Analysis and Operator Theory, Vol. 12, Issue. 6, p. 1481.

CrossRef

Google Scholar

Krantz, Steven G. and Rao, Arni S.R. Srinivasa 2020. Level of underreporting including underdiagnosis before the first peak of COVID-19 in various countries: Preliminary retrospective results based on wavelets and deterministic modeling. Infection Control & Hospital Epidemiology, Vol. 41, Issue. 7, p. 857.

CrossRef

Google Scholar

Gravey, Mathieu and Mariethoz, Grégoire 2020. QuickSampling v1.0: a robust and simplified pixel-based multiple-point simulation approach. Geoscientific Model Development, Vol. 13, Issue. 6, p. 2611.

CrossRef

Google Scholar

Zhao, Dongxiao and Aluie, Hussein 2023. Measuring scale-dependent shape anisotropy by coarse-graining: Application to inhomogeneous Rayleigh-Taylor turbulence. Physical Review Fluids, Vol. 8, Issue. 11,

CrossRef

Google Scholar

Steven G. Krantz, Washington University in St. Louis

Publisher:: Mathematical Association of America
Online publication date:: June 2014
Print publication year:: 1999
Online ISBN:: 9781614440260
DOI:: https://doi.org/10.5948/UPO9781614440260

Subjects:: Mathematics, Real and Complex Analysis
Series:: Carus Mathematical Monographs

Export citation

Information

Contents

Metrics

A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of wavelets-one of the newest ideas in the subject. A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.

Metrics

Total number of HTML views: 0

Total number of PDF views: 0 *

Loading metrics...

Total views: 0 *

Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

A Panaroma of Harmonic Analysis

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Book description

Refine List

Actions for selected content:

Contents

Frontmatter
pp i-vi

Dedication
pp vii-viii

Contents
pp ix-xii

Preface
pp xiii-xvi

0 - Overview of Measure Theory and Functional Analysis
pp 1-30

1 - Fourier Series Basics
pp 31-94

2 - The Fourier Transform
pp 95-120

3 - Multiple Fourier Series
pp 121-170

4 - Spherical Harmonics
pp 171-198

5 - Fractional Integrals, Singular Integrals, and Hardy Spaces
pp 199-234

6 - Modern Theories of Integral Operators
pp 235-272

7 - Wavelets
pp 273-312

8 - A Retrospective
pp 313-314

Appendices and Ancillary Material

Appendix I - The Existence of Testing Functions and Their Density in Lp
pp 315-317

Appendix II - Schwartz Functions and the Fourier Transform
pp 317-317

Appendix III - The Interpolation Theorems of Marcinkiewicz and Riesz-Thorin
pp 318-319

Appendix IV - Hausdorff Measure and Surface Measure
pp 320-322

Appendix V - Green's Theorem
pp 323-323

Appendix VI - The Banach-Alaoglu Theorem
pp 323-324

Appendix VII - Expressing an Integral in Terms of the Distribution Function
pp 324-324

Appendix VIII - The Stone-Weierstrass Theorem
pp 324-325

Appendix IX - Landau's O and o Notation
pp 325-326

Table of Notation
pp 327-338

Bibliography
pp 339-346

Index
pp 347-357

Metrics

Full text views

Book summary page views

A Panaroma of Harmonic Analysis

Book description

Refine List

Actions for selected content:

Save Search

Contents

Metrics

Full text views

Book summary page views