A Panorama of Harmonic Analysis (Carus Mathematical Monographs, Series Number 27)

Annotation Tracing a path from the earliest beginnings of Fourier series through to the latest research A Panorama of Harmonic Analysis discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax is a consideration of ideas from the point of view of spaces of homogeneous type, which culminates in a discussion of wavelets. This book is intended for graduate students and advanced undergraduates, and mathematicians of whatever background who want a clear and concise overview of the subject of commutative harmonic analysis 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. This Book 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 Commutative 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.

We take it for granted that the reader of this book has some acquaintance with elementary real analysis.