Ebook: Twentieth Century Harmonic Analysis — A Celebration
- Tags: Analysis
- Series: NATO Science Series 33
- Year: 2001
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
Almost a century ago, harmonic analysis entered a (still continuing) Golden Age, with the emergence of many great masters throughout Europe. They created a wealth of profound analytic methods, to be successfully exploited and further developed by succeeding generations. This flourishing of harmonic analysis is today as lively as ever, as the papers presented here demonstrate. In addition to its own ongoing internal development and its basic role in other areas of mathematics, physics and chemistry, financial analysis, medicine, and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavours, including telephone, radio, television, radar, sonar, satellite communications, medical imaging, the Internet, and multimedia. This ubiquitous nature of the subject is amply illustrated.
The book not only promotes the infusion of new mathematical tools into applied harmonic analysis, but also to fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights.
Almost a century ago, harmonic analysis entered a (still continuing) Golden Age, with the emergence of many great masters throughout Europe. They created a wealth of profound analytic methods, to be successfully exploited and further developed by succeeding generations. This flourishing of harmonic analysis is today as lively as ever, as the papers presented here demonstrate. In addition to its own ongoing internal development and its basic role in other areas of mathematics, physics and chemistry, financial analysis, medicine, and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavours, including telephone, radio, television, radar, sonar, satellite communications, medical imaging, the Internet, and multimedia. This ubiquitous nature of the subject is amply illustrated.
The book not only promotes the infusion of new mathematical tools into applied harmonic analysis, but also to fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights.
Almost a century ago, harmonic analysis entered a (still continuing) Golden Age, with the emergence of many great masters throughout Europe. They created a wealth of profound analytic methods, to be successfully exploited and further developed by succeeding generations. This flourishing of harmonic analysis is today as lively as ever, as the papers presented here demonstrate. In addition to its own ongoing internal development and its basic role in other areas of mathematics, physics and chemistry, financial analysis, medicine, and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavours, including telephone, radio, television, radar, sonar, satellite communications, medical imaging, the Internet, and multimedia. This ubiquitous nature of the subject is amply illustrated.
The book not only promotes the infusion of new mathematical tools into applied harmonic analysis, but also to fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
On the Uncertainty Principle in Harmonic Analysis....Pages 3-29
Operator Theory and Harmonic Analysis....Pages 31-56
Probabilities and Baire’s theory in harmonic analysis....Pages 57-72
Representations of Gabor frame operators....Pages 73-101
Does Order Matter....Pages 103-125
Wavelet expansions, function spaces and multifractal analysis....Pages 127-144
Some Plots of Bessel Functions of Two Variables....Pages 145-149
Lesser Known FFT Algorithms....Pages 151-162
The Phase Problem of X-ray Crystallography....Pages 163-171
Multiwindow Gabor-type Representations and Signal Representation by Partial Information....Pages 173-199
Some polynomial extremal problems which emerged in the twentieth century....Pages 201-233
The Problem of Efficient Inversions and Bezout Equations....Pages 235-269
Harmonic Analysis as found in Analytic Number Theory....Pages 271-293
Mathematics of Radar....Pages 295-328
The Mathematical Theory of Wavelets....Pages 329-366
Front Matter....Pages 367-367
Assorted Problems....Pages 369-386
How to Use the Fourier Transform in Asymptotic Analysis....Pages 387-401
Back Matter....Pages 403-412
Almost a century ago, harmonic analysis entered a (still continuing) Golden Age, with the emergence of many great masters throughout Europe. They created a wealth of profound analytic methods, to be successfully exploited and further developed by succeeding generations. This flourishing of harmonic analysis is today as lively as ever, as the papers presented here demonstrate. In addition to its own ongoing internal development and its basic role in other areas of mathematics, physics and chemistry, financial analysis, medicine, and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavours, including telephone, radio, television, radar, sonar, satellite communications, medical imaging, the Internet, and multimedia. This ubiquitous nature of the subject is amply illustrated.
The book not only promotes the infusion of new mathematical tools into applied harmonic analysis, but also to fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
On the Uncertainty Principle in Harmonic Analysis....Pages 3-29
Operator Theory and Harmonic Analysis....Pages 31-56
Probabilities and Baire’s theory in harmonic analysis....Pages 57-72
Representations of Gabor frame operators....Pages 73-101
Does Order Matter....Pages 103-125
Wavelet expansions, function spaces and multifractal analysis....Pages 127-144
Some Plots of Bessel Functions of Two Variables....Pages 145-149
Lesser Known FFT Algorithms....Pages 151-162
The Phase Problem of X-ray Crystallography....Pages 163-171
Multiwindow Gabor-type Representations and Signal Representation by Partial Information....Pages 173-199
Some polynomial extremal problems which emerged in the twentieth century....Pages 201-233
The Problem of Efficient Inversions and Bezout Equations....Pages 235-269
Harmonic Analysis as found in Analytic Number Theory....Pages 271-293
Mathematics of Radar....Pages 295-328
The Mathematical Theory of Wavelets....Pages 329-366
Front Matter....Pages 367-367
Assorted Problems....Pages 369-386
How to Use the Fourier Transform in Asymptotic Analysis....Pages 387-401
Back Matter....Pages 403-412
....