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Literature Cited
N. S. Landkof, Foundations of Modern Potential Theory, Springer, Berlin (1972).
A. I. Plotkin, “On isometric operators on subspaces of Lp spaces,” Dokl. Akad. Nauk SSSR,193, No. 3, 537–539 (1970).
A. I. Plotkin, “The continuation of Lp-isometries,” J. Sov. Math.,2, No. 2 (1974).
W. Rudin, “Lp-isometries and equimeasurability,” Indiana Univ. Math. J.,25, No. 3, 215–228 (1976).
A. N. Al-Hussaini, “Potential operators and equimeasurability,” Pac. J. Math.,76, No. 1, 1–7 (1978).
C. D. Hardin, Jr., “Isometries on subspaces of Lp,” Indiana Univ. Math. J.,30, No. 3, 449–465 (1981).
W. Linde, “Moments of measures on Banach spaces,” Math Ann.,258, 277–287 (1982).
W. Lusky, “Some consequences of Rudin's paper ‘Lp-isometries and equimeasurability’,” Indiana Univ. Math. J.,27, No. 5, 859–866 (1978).
A. I. Plotkin, “Isometric operators in Lp spaces of analytic and harmonic functions,” J. Sov. Math.,4, No. 4 (1975).
A. I. Plotkin, “An algebra that is generated by translation operators, and Lp-norms,” Funkts. Analiz, Ul'yanovsk, No. 6, 112–121 (1976).
A. L. Koldobskii, “The continuation of isometries in Orlicz spaces,” in: Gertsenovskie Chteniya, Matematika, Leningrad (1977), pp. 61–66.
K. Stephenson, “Certain integral equalities which imply equimeasurability of functions,” Can. J. Math.,29, No. 4, 827–844 (1977).
A. L. Koldobskii, “On isometric operators in Lp(x,R n),” Funkts. Analiz, Ul'yanovsk, No. 12, 90–99 (1979).
A. L. Koldobskii, “On isometric operators in vector-valued Lp spaces,” J. Sov. Math.,36, No. 3 (1987).
A. L. Koldobskii, “A uniqueness theorem for measures in C(K) and its application to the theory of random processes,” J. Sov. Math.,27, No. 5 (1984).
W. K. Hayman and P. B. Kennedy, Subharmonic Functions, Academic Press, London (1976).
B. Ya. Levin, Entire Functions [in Russian], Moscow State Univ. (1971).
Yu. A. Brudnyi and E. A. Gorin, Isometric Representations and Differential Inequalities [in Russian], Yaroslav State Univ (1981).
E. A. Gorin and A. L. Koldobskii, “On potential identifying measures in Banach spaces,” Dokl. Akad. Nauk SSSR,285, No. 2, 270–274 (1985).
W. Rudin, Functional Analysis, McGraw-Hill, New York (1973).
I. M. Gel'fand and G. E. Shilov, Generalized Functions. Vol. 1: Properties and Operations, Academic Press, New York (1964).
H. Bateman and A. Erdelyi, Higher Transcendental Functions, Vols. I–III, McGraw-Hill, New York (1953–1955).
N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory, Interscience, New York (1958).
P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).
J. Hoffman-Jφrgensen, “Measures which agree on balls,” Math. Scand.,37, No. 2, 319–326 (1975).
J. P. R. Christensen, “The small ball theorem for Hilbert spaces,” Math. Ann.,237, 273–276 (1978).
E. C. Titchmarsh, The Theory of Functions, Oxford Univ. Press (1939).
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series [in Russian], Nauka, Moscow (1981).
N. I. Akhiezer, The Classical Moment Problem and Some Related Questions in Analysis, Oliver and Boyd, Edinburgh (1965).
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Moscow. Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 28, No. 1, pp. 65–80, January–February, 1987.
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Gorin, E.A., Koldobskii, A.L. On potentials of measures in Banach spaces. Sib Math J 28, 46–58 (1987). https://doi.org/10.1007/BF00970208
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DOI: https://doi.org/10.1007/BF00970208