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On generalized eigenfunctions of an operator which is related to a problem of S. L. Sobolev. (English. Russian original) Zbl 0195.39103
Sib. Math. J. 9(1968), 798-811 (1969); translation from Sib. Mat. Zh. 9, 1075-1092 (1968).

Full Text: DOI
[1] S. L. Sobolev, ?Motion of a symmetric top filled with a liquid,? Prikl. Mekh. i Tekhn. Fiz., No. 3, 20-55 (1960).
[2] S. L. Sobolev, ?A new problem of mathematical physics,? Izv. Akad. Nauk SSSR, Ser. Matem.,18, No. 1, 3-50 (1954). · Zbl 0055.08401
[3] S. L. Sobolev, ?Sur une classe des problemes de physique mathematique,? 48 Riunionne della Societa Italiana per ll Pregresso della Science, Rome (1965), 192-208.
[4] T. I. Zelenyak, ?Dependence on the boundary for solutions of some mixed problems for equations of small vibrations in a rotating liquid,? Dokl. Akad. Nauk SSSR,164, No. 6, 1225-1228 (1965).
[5] V. N. Maslennikova, ?An explicit solution of the Cauchy problem for a system of partial differential equations of first order,? Izv. Akad. Nauk SSSR, Ser. Matem.,22, No. 1, 135-160 (1958). · Zbl 0078.08301
[6] V. N. Maslennikova, ?Mixed problems for a system of partial differential equations of first order,? Izv. Akad. Nauk SSSR, Ser. Matem.,22, No. 3, 271-298 (1958). · Zbl 0081.31101
[7] R. A. Aleksandryan, Dependence of Qualitative Properties of Solutions of Mixed Problems on the Shape of the Domain. Dissertation [in Russian], MGU, Moscow (1949).
[8] Yu. M. Berezanskii, Expansions in Terms of Eigenfunctions of a Self-adjoint Operator [in Russian], Naukova Dumka, Kiev (1965).
[9] R. A. Aleksandryan, ?A Sobolev problem for special partial differential equations of fourth order,? Dokl. Akad. Nauk SSSR,73, No. 4, 631-634 (1950).
[10] R. A. Aleksandryan, ?Mixed problems for aclass of systems of differential equations of Sobolev type,? Trudy Vsesoyuzogo Soveshchaniya po Differentsiallnym Uravheniyam, Erevan, November, 1958.
[11] R. A. Aleksandryan, ?On the correctness of a mixed problem and the spectral equivalence of two operators connected with it,? Izv. Akad. Nauk ArmSSR,10, No. 1, 63-69 (1957).
[12] R. A. Aleksandryan, ?The Dirichlet problem and the completeness of a system of functions on the cirele,? Dokl. Akad. Nauk SSSR,73, No. 5, 869-872 (1950).
[13] R. A. Aleksandryan, ?Spectral properties of operators generated by systems of differential equations of Sobolev type,? Trudy Moscow Matem. ob-va,9, 455-505 (1960).
[14] T. I. Zelenyak, ?The behavior of a solution of a Sobolev problem as t??,? Dokl. Akad. Nauk SSSR,139, No. 3, 531-533 (1961). · Zbl 0128.32703
[15] T. I. Zelenyak, ?A Sobolev problem,? Dokl. Akad. Nauk SSSR,147, No. 5, 1017-1019 (1952).
[16] T. I. Zelenyak, ?Invariant subspaces of an operator,? Sibirsk. Matem. Zh.,3, No. 3, 471-475 (1962).
[17] T. I. Zelenyak, ?A mixed problem for an equation which is not solvable with respect to higher time derivatives,? Dokl. Akad. Nauk SSSR,158, No. 6, 1268-1270 (1964). · Zbl 0142.37801
[18] T. I. Zelenyak, ?Asymptotic behavior of solutions of a mixed problem,? Differential Equations.2. No. 1, 47-64 (1966). · Zbl 0142.06104
[19] F. John, ?The Dirichlet problem for a hyperbolic equation,? Amer. J. Math.,63, 141-154 (1941). · Zbl 0024.20304
[20] D. G. Bourgin and K. Duffin, ?The Dirichlet problem for the vibrating string equations,? Bull. Amer. Math. Soc.,45, 851-859 (1939). · Zbl 0023.04201
[21] N. N. Vakhaniya, ?A boundary value problem with values given on the whole boundary for a hyperbolic system, equivalent to the equation of a vibrating string,? Dokl. Akad. Nauk SSSR,116, No. 6, 906-909 (1957). · Zbl 0084.09001
[22] R. T. Denchev, ?The spectrum of an operator,? Dokl. Akad. Nauk SSSR,126, No. 2, 259-262 (1959). · Zbl 0089.30602
[23] A. Huber, ?Die erste Randwertaufgabe für geschlos sone Bereiche bei der Gleichung ?z/?x by f(x, y)?, Monats Math. Phys.39, 79-100 (1932) · Zbl 0004.11501
[24] V. L. Arnol’d, ?Small denominators,? Izv. Akad. Nauk SSSR, Ser. Matem.25, No. 1, 21-86 (1961).
[25] A. Poincaré, On Curves Defined by Differential Equations [Russian translation], Moscow-Leningrad (1947).
[26] A. Denjoy, ?Sur les corbes definles par les equations differenticlles a la suriace du tore,? Journ. de Math.,11, No. 4, 333-375 (1932). · JFM 58.1124.04
[27] E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York (1955). · Zbl 0064.33002
[28] A. Finzi, ?Sur le probleme de la generation d’une transformation donnee d’une courbe fermee par une transformation infinitesrmall.? Ann. Ecole Norm. Sup.,69, 371-430 (1952). · Zbl 0048.25901
[29] R. A. Aleksandryan, ?Construction of a complete collection of solutions of a homogeneous Dirichlet problem for the equation of a vibrating string,? Dokl. Akad. Nauk SSSR,162, No. 2, 247-251 (1965). · Zbl 0138.34802
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