Explorations in Harmonic Analysis

With Applications to Complex Function Theory and the Heisenberg Group

By:

Steven G Krantz

Format:

Hardback

Series:

Applied and Numerical Harmonic Analysis

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Description

Harmonic analysis is a venerable part of modern mathematics. Its roots began, perhaps, with late eighteenth-century discussions of the wave equation. Using the method of separation of variables, it was realized that the equation could be solved with a data function of the form?(x)= sin jx for j? Z.Itwasnaturaltoask, using the philosophy of superposition, whether the equation could then be solved with data on the interval [0,?] consisting of a nite linear combinationof the sin jx. With an af rmative answer to that question, one is led to ask about in?nite linear combinations. This was an interesting venue in which physical reasoning interacted with mathematical reasoning. Physical intuition certainly suggests that any continuous function? can be a data function for the wave equation. So one is led to ask whether any continuous? can be expressed as an (in nite) superposition of sine functions. Thus was born the fundamental question of Fourier series. No less an eminence gris than Leonhard Euler argued against the proposition.

Release date NZ

May 5th, 2009

Author

Steven G Krantz

Audiences

Postgraduate, Research & Scholarly
Undergraduate

Illustrations

XIV, 362 p.

Pages

362

Series

Applied and Numerical Harmonic Analysis

Dimensions

156x234x22

ISBN-13

9780817646684

Product ID

3041331

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