Chapter. Downloads Download to read the full chapter text. Cite chapter Gelfand, I.M. & Shilov, G.E. () Generalised Functions. Academic Press. by I. M. Gel'fand (Author), G. E. Shilov (Author) Generalized Functions, Volume 2: Spaces of Fundamental and Generalized Functions (Ams I. M. Gelfand. AMS Chelsea Publishing: An Imprint of the American Mathematical Society. The first systematic theory of generalized functions (also known as.
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PDF | I. M. Gelfand and G. E. Shilov [GS] introduced the Gelfand-Shilov spaces of type S, generalized type S and type W of test functions to. representation theory, xvii + pp.; by I. M. Gel'fand and G. E. Shilov,. Academic At the beginning of the 's the theory of generalized functions was in somewhat think this is attributable to the fact that Gelfand and his co-authors are. Generalized Functions, Volume 5: Integral Geometry and Gelfand, I M; Shilov, Georgi E; Graev, M I; Vilenkin, N Y; Pyatetskii-Shapiro, I I.
Differentiation in S. Regularization of Functions with Algebraic Singularities 3.
The Generalized Functions x and xt. IndefnieImearals of 24 xIsanx 3. Normalization of x2, x4 x!
Canonical Regularization. Regularization of Other Integrals The Generalized Function?
Plane-Wave Expansion of aor ters 3. Homogeneous Functions 4, Associate Functions Definition Taylor's and Laurent Series for x4 and x2.
Expansion of x? Expansion of r. Convolutions of Generalized Functions 5. Direct Product of Generalized Functions 5. Elementary Solutions of Regular Homogeneous Equa- tions Elementary Solutions of Cauchy's Problem Appendix 1.
Differentiable Functions. Fourier Transforms of Funetions in K. The Space Zs. Fourier Transforms of Functions in S.. Fourier Transforms of Generalized Functions.
A Single Variable Fourier Transforms of xi, 2, [and ['snx Vindas, On weighted inductive limits of spaces of ultradifferentiable functions and their duals, Math. Debrouwere, H. Vernaeve, J.
Vindas, A non-linear theory of infrahyperfunctions, Kyoto J. Vindas, Optimal embeddings of ultradistributions into differential algebras, Monatsh.
Vindas, On the non-triviality of certain spaces of analytic functions. Hyperfunctions and ultrahyperfunctions of fast growth , Rev.
Gelfand shilov generalized functions pdf
Debrouwere, E. Nigsch, Sheaves of nonlinear generalized function spaces, New York J.
Vindas, Solution to the first Cousin problem for vector-valued quasianalytic functions, Ann. Pura Appl.
Debrouwere, Generalized function algebras containing spaces of periodic ultradistributions, in: Generalized Functions and Fourier Analysis, pp. Theory Adv.
Vindas, Discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type, J. D thesis A. Debrouwere, Contributions to the linear and non-lineary theory of ultradistributions, Dissertation, Ghent University, My main interests are: Linear and non-linear generalized function spaces Classes of smooth functions Homological methods in functional analysis See my research statement for a more detailed account.
Curriculum Vitae Click here to download my CV. Talks Whitney's extension theorem.
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Equations with Coefficients Which Depend on x Appendix 3.