A Guide to Distribution Theory and Fourier TransformsThis book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudo-differential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book. in applied analysis and mathematical physics. |
Contents
The Calculus of Distributions | 11 |
Fourier Transforms | 26 |
Fourier Transforms of Tempered Distributions | 43 |
Copyright | |
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Other editions - View all
A Guide to Distribution Theory and Fourier Transforms Robert S. Strichartz No preview available - 2003 |
Common terms and phrases
adjoint identity analytic function approximate argument boundary bounded boundedness change of variable compact support condition continuous function converges convolution cotangent curve cut-off function derivatives differential equation differential operator direction distribution of compact distribution theory elliptic operators estimate example expansion fact finite number Fourier inversion formula Fourier series Fourier transform function f ƒ and g Gaussian homogeneous of degree hyperbolic implies integrable function linear locally integrable means microlocally smooth multiplication neighborhood nonnegative obtain open set parametrix Plancherel formula Poisson summation formula polynomial positive definite positive distribution problem radial rapidly decreasing restriction Riemann-Lebesgue lemma satisfies sing supp singularities Sobolev inequality Sobolev spaces solve sphere structure theorem tempered distribution test functions uncertainty principle vanishes at infinity wave equation wave front set wavelet zero მე მუ