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Doklady Mathematics

, Volume 98, Issue 3, pp 541–544 | Cite as

Distributions and Analytical Measures on Infinite-Dimensional Spaces

  • A. A. BelyaevEmail author
  • O. G. Smolyanov
Mathematics
  • 3 Downloads

Abstract

Spaces of test functions and spaces of distributions (generalized measures) on infinite-dimensional spaces are constructed, which, in the finite-dimensional case, coincide with classical spaces \(\mathscr{D}\) and \(\mathscr{D}'\). These distribution spaces contain generalized Feynman measures (but do not contain a generalized Lebesgue measure, which is not considered in this paper). For broad classes of infinite-dimensional differential equations in distribution spaces, the Cauchy problem has fundamental solutions. These results are much more definitive than those of A.Yu. Khrennikov’s and A.V. Uglanov’s pioneering works.

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Financial University under the Government of the Russian FederationMoscowRussia
  2. 2.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  3. 3.Moscow Institute of Physics and Technology (State University)Dolgoprudnyi, Moscow oblastRussia

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