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References
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).
A. N. Tikhonov, “Uniqueness theorems for the heat equation,” Mat. Sb.,42, No. 2, 199–216 (1935).
V. P. Mikhaîlov, Partial Differential Equations [in Russian], Nauka, Moscow (1983).
J. Schauder, “Über lineare elliptische Differentialgleichungen zweiter Ordnung,” Math. Z.,38, No. 2, 257–282 (1934).
V. A. Solonnikov, “On boundary value problems for linear parabolic systems of general differential equations,” Trudy Mat. Inst. Akad. Nauk SSSR,83, 3–162 (1965).
O. A. Ladyzhenskaya and V. A. Solonnikov, “The linearization principle and invariant manifolds for problems of magnetohydrodynamics,” Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI),38, 46–93 (1973).
V. S. Belonosov, “Estimates for solutions to nonlinear parabolic systems in weighted Hölder classes and some of their applications,” Mat. Sb.,110, No. 2, 163–188 (1979).
M. I. Matiîchuk and S. D. Èîdel’man, “On parabolic systems with coefficients satisfying Dini’s condition,” Dokl. Akad. Nauk SSSR,165, No. 3, 482–485 (1965).
M. I. Matiîchuk and S. D. Èîdel’man, On parabolic systems with Dini continuous coefficients,” in: Proceedings of a Seminar on Functional Analysis [in Russian], Voronezhsk. Univ., Voronezh, 1967, 9.
M. I. Matiîchuk and S. D. Èîdel’man, “The Cauchy problem for parabolic systems whose coefficients have low smoothness,” Ukrain. Mat. Zh.,22, No. 1, 22–36 (1970).
A. N. Tikhonov and A. A. Samarskiî, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1977).
Ch. J. Vallée Poussin, de la, Leçons sur l’Approximation des Fonctions d’une Variable Réelle, Paris (1919).
A. Zygmund, “O module ciaglosci sumy szeregu sprzezonego z szeregiem Fouriera,” Prace Mat.-Fiz.,33, 125–132 (1924).
N. K. Bari and S. B. Stechkin, “Best approximations and differential properties of two conjugate functions,” Trudy Moskov. Mat. Obshch.,5, 483–522 (1956).
J. Privaloff, “Sur les fonctions conjuguées,” Bull. Soc. Math. France,44, 100–103 (1916).
A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, New York (1964).
S. M. Lozinskiî, “The converse of Jackson’s theorem,” Dokl. Akad. Nauk SSSR,83, No. 5, 645–647 (1952).
S. N. Bernshteîn, Collected Works. Vol. 2: The Constructive Theory of Functions, (1931–1953) [in Russian], Izdat. Akad. Nauk SSSR, Moscow (1954).
S. M. Nikol’skii, “The Fourier series of a function with given continuity modulus,” Dokl. Akad. Nauk SSSR,52, No. 3, 191–194 (1946).
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The research was supported by the Russian Foundation for Basic Research (Grant 97-01-00508) and the State Maintenance Program for Leading Scientific Schools of the Russian Federation (Grant 96-15-96290).
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 39, No. 2, pp. 243–260, March–April, 1998.
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Akhmetov, D.R. On the isomorphism generated by the heat equation. Sib Math J 39, 209–225 (1998). https://doi.org/10.1007/BF02677507
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DOI: https://doi.org/10.1007/BF02677507