The Cross-Correlation Operation of Schwartz Distributions


A generalization of the cross-correlation operation of the Schwartz distributions is considered, and some properties of this operation are established.

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  1. 1.

    V. S. Vladimirov, Generalized Functions in Mathematical Physics [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  2. 2.

    K. Iosida, Functional Analysis, Springer, Berlin (1965).

    Google Scholar 

  3. 3.

    V. I. Parygin and V. N. Balakshii, Optical Processing of Information [in Russian], Moscow State University, Moscow (1987).

    Google Scholar 

  4. 4.

    A. P. Robertson and W. Robertson, Topological Vector Spaces, 2nd ed., Cambridge University Press, Cambridge (1973).

    Google Scholar 

  5. 5.

    A. Grothendieck, “Produits tensoriel topologues et espaces nucleaire, ” Mem. Amer. Math. Soc., 16, No. 11, 1–140 (1955).

    Google Scholar 

  6. 6.

    S. V. Sharin and O. V. Lopushansky, “Operator calculus for convolution algebras of Schwartz distributions on the semiaxis, ” Transactions of the Lviv Mathematical Society, Mathematical Studies, 7, No. 1, 61–72 (1997).

    Google Scholar 

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Sharin, S.V. The Cross-Correlation Operation of Schwartz Distributions. Journal of Mathematical Sciences 107, 3604–3609 (2001).

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  • Schwartz Distribution