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Distributions and Analytical Measures on Infinite-Dimensional Spaces

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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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Authors and Affiliations

  1. Financial University under the Government of the Russian Federation, Moscow, 125993, Russia

    A. A. Belyaev

  2. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    O. G. Smolyanov

  3. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, 141700, Russia

    O. G. Smolyanov

Authors
  1. A. A. Belyaev
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  2. O. G. Smolyanov
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Corresponding author

Correspondence to A. A. Belyaev.

Additional information

Original Russian Text © A.A. Belyaev, O.G. Smolyanov, 2018, published in Doklady Akademii Nauk, 2018, Vol. 483, No. 1.

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Belyaev, A.A., Smolyanov, O.G. Distributions and Analytical Measures on Infinite-Dimensional Spaces. Dokl. Math. 98, 541–544 (2018). https://doi.org/10.1134/S1064562418070013

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  • DOI: https://doi.org/10.1134/S1064562418070013

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