Review
...an in-depth and up-to-date survey of much of the analysis concerning distributional and ultradistributional integral transforms...a valuable addition to the literature.
–Richard D. Carmichael of Department of Mathematics and Computer Science, Wake Forest University
Product Description
For those who have a background in advanced calculus, elementary topology and functional analysis - from applied mathematicians and engineers to physicists - researchers and graduate students alike - this work provides a comprehensive analysis of the many important integral transforms and renders particular attention to all of the technical aspects of the subject. The author presents the last two decades of research and includes important results from other works.
With a description in Chapter 1 of foundational, topological information for the study of the distributions (generalized functions) and ultradistributions to be considered, including the structure of these distributions, the author then moves on to an analysis of the transforms and ends with a discussion of the eigenfunction expansion of generalized functions. Applications of the transforms to various mathematical, physical, and engineering problems are given, and open research problems present a challenge to the reader. An extensi
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Inside This Book
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First Sentence:
This chapter serves as a brief introduction to ideas from the theory of locally convex spaces. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
countably multinormed space, ultradifferentiable functions, multinormed spaces, countable union space, regular generalized function, following inversion theorem, trigonometric kernels, dual integral equations, distributional boundary values, countably normed spaces, continuous linear mapping, separating collection, abelian theorems, test function spaces, generalized functions, inversion formulae, delta functional, following uniqueness result, boundedness property, asymptotic orders, fractional integrals, operational calculus, tempered distribution, final value theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof See Zemanian, Proof See Barros-Neto, Proof By Theorem, Taking the Laplace, Using the Inversion Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter serves as a brief introduction to ideas from the theory of locally convex spaces. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
countably multinormed space, ultradifferentiable functions, multinormed spaces, countable union space, regular generalized function, following inversion theorem, trigonometric kernels, dual integral equations, distributional boundary values, countably normed spaces, continuous linear mapping, separating collection, abelian theorems, test function spaces, generalized functions, inversion formulae, delta functional, following uniqueness result, boundedness property, asymptotic orders, fractional integrals, operational calculus, tempered distribution, final value theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof See Zemanian, Proof See Barros-Neto, Proof By Theorem, Taking the Laplace, Using the Inversion Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 40
books:
See all 40 books this book cites
5
books
cite this book:
- Laplace Transform by D. V. Widder on page 118, and Back Matter
- Singular Integral Equations by N.I. Muskhelishvili in Back Matter
- in Back Matter
- Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by Walter Rudin in Back Matter
- Linear Partial Differential Equations (Notes on Mathematics and Its Applications) by F. Treves in Back Matter
See all 40 books this book cites
- Wavelets and Allied Topics by Pawan K. Jain on page 71
- H-Transforms: Theory and Applications (Analytical Methods and Special Functions, 9) by Anatoly A. Kilbas in Back Matter
- A Course in Distribution Theory and Applications by R. S. Pathak in Back Matter
- Function Spaces and Applications by David E. Edmunds on page 243
- Analysis and Applications by H. P. Dikshit on page 233
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