Abstract
In this paper we present the necessary and sufficient condition of epimorphism of the operator
where the Qi(d) are differential operators with constant coefficients, Rm is a subspace of Rn, and Hμ(Rn) and Hvi(Rm) are distribution spaces introduced in [1]. We prove the existence of a linear continuous operator π which is the right inverse of
. There are 4 references.
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L. Volevich and B. Paneyakh, Some spaces of generalized functions and embedding theorems, Uspekhi Matem. Nauk,20, No. 1, 3–74 (1965).
B. Paneyakh, Some inequalities for functions of exponential type and a priori bounds for general differential operators, Uspekhi Matem. Nauk,21, No. 3, 75–114 (1966).
L. Slobodetskii, Generalized Sobolev spaces and their use in boundary-value problems, Uch. Zap. Leningr. Ped. Inst.,197, 54–112 (1958).
M. Itano, On a trace theorem for the spaces Hμ(Rn), J. Sci. Hiroshima Univ.,30, No. 1, 11–29 (1966).
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Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 577–588, December, 1967.
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Paneyakh, B.P. Theorems about traces and the extension of distributions. Mathematical Notes of the Academy of Sciences of the USSR 2, 844–850 (1967). https://doi.org/10.1007/BF01473463
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DOI: https://doi.org/10.1007/BF01473463