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Harmonic analysis and fractal analysis over local fields and applications/ Weiyi Su

By: Publication details: Singapore: World Scientific, 2018Description: xii,318 pages, 23 cmISBN:
  • 9789813200494
Subject(s): DDC classification:
  • 23 512.7 W415
Contents:
Preliminary -- Character Group Γp of Local Field Kp -- Harmonic Analysis on Local Fields -- Function Spaces on Local Fields -- Fractal Analysis on Local Fields -- Fractal PDE on Local Fields -- Applications to Medicine Science --
Summary: This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field. The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 512.7 W415 (Browse shelf(Opens below)) Available 138550
Total holds: 0

Preliminary --
Character Group Γp of Local Field Kp --
Harmonic Analysis on Local Fields --
Function Spaces on Local Fields --
Fractal Analysis on Local Fields --
Fractal PDE on Local Fields --
Applications to Medicine Science --

This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field.
The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.

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