Abstract
We study the regularizability of mappings that are inverses of integral operators acting fromC(0,1) toL 2(0,1) and possessing noninjective continuation toL 2(0,1). We construct classes of such operators with regularizable as well as nonregularizable inverses for which the continuation of the operators toL 2(0,1) has an infinite-dimensional kernel.
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V. P. Tanana, “The solution of Fredholm integral equations of the first kind in the spaceC(0,1),”Ural. Gos. Univ. Mat. Zap.,7, No. 4, 83–90 (1970).
L. D. Menikhes, “The regularizability of mappings that are inverse to integral operators,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],241, No. 2, 282–285 (1978).
A. N. Plichko, “Nonnorming subspaces and integral operators with a nonregularizable inverse,”Sibirsk. Mat. Zh., [Siberian Math. J.],29, No. 4, 208–211 (1988).
M. I. Ostrovskii, “A note on the analytical representability of mappings that are inverses of linear integral operators,”Mat. Fizika, Analiz, Geometriya,1, No. 3–4, 513–515 (1994).
V. A. Vinokurov, Yu. I. Petunin, and A. N. Plichko, “Conditions for the measurability and regularizability of mappings that are inverses of continuous linear mappings,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl],220, No. 3, 509–511 (1975).
Yu. I. Petunin and A. N. Plichko, “Tihonov regularizability of certain classes of ill-posed problems,” in:Mathematics Collection [in Russian], Naukova Dumka, Kiev (1976), pp. 221–224.
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Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 222–229, February, 1999.
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Menikhes, L.D. Regularizability of some classes of mappings that are inverses of integral operators. Math Notes 65, 181–187 (1999). https://doi.org/10.1007/BF02679815
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DOI: https://doi.org/10.1007/BF02679815