Metric estimates of the characterictic determinant of an interpolation problem with nodes, one of which is multiple, for a linear partial differential equation (in Ukrainian) 

Author 
quaternion@ukr.net
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Lviv

Abstract 
The metric theorem of an estimations of the characteristic determinant of an interpolation
problem for linear partial differential equation with constant coeffcients are proved.

Keywords 
Diophantine approximation; Lebesgue measure; interpolation problem

DOI 
doi:10.15330/ms.43.1.8893

Reference 
1. B.I. Ptashnik, Illposed boundary value problems for partial differential equations. K.: Nauk. dumka,
1984. 264 p. (in Russian)
2. V.I. Gorbachuk, M.L. Gorbachuk, Boundary value problems for operator differential equations. Translated and revised from the 1984 Russian original. Mathematics and its Applications (Soviet Series), 48. Kluwer Academic Publishers Group, Dordrecht, 1991. xii+347 p. 3. L. H.ormander, The analysis of linear partial differential operators II. Differential operators with constant coefficients. 2nd rev. printing., 2nd rev. printing, Berlin etc.: SpringerVerlag, 1990. viii+392 p. 4. V.I. Bernik, Yu.V. Melnichuk, Diophantine approximations and Hausdorff dimension. Minsk: Nauka i tekhnika, 1988. 144 p. (in Russian) 5. V.G. Sprindzhuk, Metric theory of diophantine approximations. Series: Scripta series in mathematics. John Wiley and Sons Inc (1979). 170 p. 6. V.G. Sprindzhuk, Achievements and problems in Diophantine approximation theory, Russian Math. Surveys, 35 (1980), 180. 7. A.Ya. Khinchin, Continued fractions, Chicago: University of Chicago Press, 1964. 8. B.Yo. Ptashnyk, M.M. Symotyuk, Multipoint problem for nonisotropic partial differential equations with constant coefficients, Ukrainian Math. J., 55 (2003), Ή2, 293310; translation of Ukrain. Mat. Zh., 55 (2003), Ή2, 241254. 9. B.Yo. Ptashnyk, M.M. Symotyuk, Multipoint problem with multiple nodes for partial differential equations with constant coefficients, Ukrainian Math. J., 55 (2003), Ή3, 481497; translation of Ukrain. Mat. Zh., 55 (2003), Ή3, 400413. 10. M.M. Symotyuk, Multipoint problem for loaded polyharmonic equation, Prykl. probl. mech. and math., 1 (2003), 2534. (in Ukrainian) 11. Ph. Hartman, Ordinary differential equations. M.: Mir, 1970. 720 p. (in Russian) 
Pages 
8893

Volume 
43

Issue 
1

Year 
2015

Journal 
Matematychni Studii

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