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

M. M. Symotyuk

doi:10.15330/ms.43.1.88-93

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

1. B.I. Ptashnik, Ill-posed 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.: Springer-Verlag, 1990. viii+392 p.

4. V.I. Bernik, Yu.V. Mel’nichuk, 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), 1–80.

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), №2, 293–310; translation of Ukrain. Mat. Zh., 55 (2003), №2, 241–254.

9. B.Yo. Ptashnyk, M.M. Symotyuk, Multipoint problem with multiple nodes for partial differential equations with constant coefficients, Ukrainian Math. J., 55 (2003), №3, 481–497; translation of Ukrain. Mat. Zh., 55 (2003), №3, 400–413.

10. M.M. Symotyuk, Multipoint problem for loaded polyharmonic equation, Prykl. probl. mech. and math., 1 (2003), 25–34. (in Ukrainian)

11. Ph. Hartman, Ordinary differential equations. – M.: Mir, 1970. – 720 p. (in Russian)

	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	M. M. Symotyuk 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.43.1.88-93
Reference	1. B.I. Ptashnik, Ill-posed 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.: Springer-Verlag, 1990. viii+392 p. 4. V.I. Bernik, Yu.V. Mel’nichuk, 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), 1–80. 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), №2, 293–310; translation of Ukrain. Mat. Zh., 55 (2003), №2, 241–254. 9. B.Yo. Ptashnyk, M.M. Symotyuk, Multipoint problem with multiple nodes for partial differential equations with constant coefficients, Ukrainian Math. J., 55 (2003), №3, 481–497; translation of Ukrain. Mat. Zh., 55 (2003), №3, 400–413. 10. M.M. Symotyuk, Multipoint problem for loaded polyharmonic equation, Prykl. probl. mech. and math., 1 (2003), 25–34. (in Ukrainian) 11. Ph. Hartman, Ordinary differential equations. – M.: Mir, 1970. – 720 p. (in Russian)
Pages	88-93
Volume	43
Issue	1
Year	2015
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

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)