Abstract
The concept of a Stieltjes multiple-integral operator was first introduced by Yu. L. Daletskii and S. G. Krein [1] in connection with certain aspects of analytical perturbation theory. In a number of articles [2–5], M. Sh. Birman and M. Z. Solomyak developed the theory of double-integral operators which they found to be closely related to a variety of problems in analysis.
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Literature Cited
Yu. L. Daletskii and S. G. Krein, “Integration and differentiation of functions of Hermitian operators with applications in perturbation theory,” in: Transactions of the Voronezh Seminar on Functional Analysis [in Russian], Vol. 1, Voronezh (1956), pp. 81–205.
M. Sh. Birman and M. Z. Solomyak, “On Stieltjes double-integral operators,” Dokl. Akad. Nauk SSSR, Vol. 165, No. 6, pp. 1223–1226 (1965).
M. Sh. Birman and M. Z. Solomyak, “Stieltjes double-integral operators,” in: Topics in Mathematical Physics, Vol. 1, M. Sh. Birman (editor), Consultants Bureau, New York (1967), pp. 25–54.
M. Sh. Birman and M. Z. Solomyak, “Stieltjes double-integral operators and the problem of factors,” Dokl. Akad. Nauk SSSR, Vol. 171, No. 6 (1966).
M. Sh. Birman and M. Z. Solomyak, “Stieltjes double-integral operators. II,” in: Topics in Mathematical Physics, Vol. 2, M. Sh. Birman (editor), Consultants Bureau, New York (1968), pp. 19–46.
B. S. Pavlov, “On multidimensional integral operators,” Present Volume, p.
K. Töllner, “Some properties of transformers defined by double-integral operators,” Present Volume, p. 81.
I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Nonself-Adjoint Operators [in Russian], Izd. “Nauka,” Moscow (1966).
A. Zigmund, Trigonometric Series, Vols. I and II [Russian translation], Izd. “Mir,” Moscow (1965).
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© 1971 Consultants Bureau, New York
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Solomyak, M.Z., Sten’kin, V.V. (1971). On One Class of Stieltjes Multiple-Integral Operators. In: Smirnov, V.I. (eds) Linear Operators and Operator Equations. Problems in Mathematical Analysis / Problemy Matematicheskogo Analiza / Πроблемы Математического Анализа. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0013-8_5
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