A nonstandard difference Sturm-Liouville operator

• Autorzy: Javorskij, J. , Ljance, V.
• Języki publikacji: EN

Abstrakty

EN

After Nelson's Radically Elementary Probability Theory [1] a natural question arises: whether a hyperfinite-dimensional space is sufficiently rich to be used for the same goal as an infinite-dimensional one. Here a hyperfinite 3-diagonal matrix is investigated, which spectral properties are simular to the Naimarks's singular nonselfadjoint Sturm-Liouville differential operator on semi-axis [2, 3].

Słowa kluczowe

PL

operator samosprzężony; teoria operatora

EN

algebraic multiplicity; continuous spectrum; difference operator; eigenfunction; eigenprojector; eigenvalue; infinitesimal; Jose function; nonstandard operator theory; operator theory; principal function; resolvent; selfadioint operator; special classes of linear operators; spectral singularity; spectrum; standard; Sturm-Liouville operator

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no 3
• Strony: 285--290
• Opis fizyczny: Bibliogr. 10 poz.,

Twórcy

autor

Javorskij, J.

• Department of Mathematics, Lviv State University, Lviv, 290602, UKRAINE

autor

Ljance, V.

• Department of Mathematics, Lviv State University, Lviv, 290602, UKRAINE ,

Bibliografia

• [1] E. Nelson, Radicaddy Elementary Probability Theory, Princeton University Press, 1987.
• [2] V. E. Lyantse, The non-selfadjoint differential operator of the second order on the half-axis, Appendix 2 in the book M. A. Naimark, Linear differential operators, Part 2, F. Ungar Publishing CO, New York (1968) 292-331.
• [3] M. A. Naimark, Investigation of the spectrum and expansion in eigenfunctions of a non-selfadjoint differential operator of the 2nd order on the half-axis (in Russian), Trudу, Moskow, Math. Obsch., 3 (1954) 181-270.
• [4] E. Nelson, Internal Set Theory, Bull. Amer. Math. Soc., 83 (1977) 1165-1198.
• [5] V. A. Marchenko, Eigenfunction expansions for non-selfadjoint singular differential operators of the second order (in Russian), Mat. Sb., 52 (94) (1960) 739-788.
• [6] N. Dunford, J. Schwartz, Linear operators, Part 3: Spectral operators, Wiley Interscience, New York-London-Sydney-Toronto 1971.
• [7] V. E. Lyantse, On the differential operator with the spectral singularities (in Russian), Mat. Sb., 64 (4) (1964) 521-561, 65 (1) (1964) 47-103.
• [8] V. E. Lyantse, Expansion in eigenfunction, Rev. Roum. Math. Pures et Appl., 11 (8) (1966) 921-950, 11 (10) (1966) 1187-1224.
• [9] V. E. Lyantse, Perturbation of continuous spectrum (in Russian), Dokl. Acad. Nauk SSSR, 187 (1969) 514-517.
• [10] V. A. Blashchak, On the second-order differential operator on the whole axis with the spectral singularities (in Russian), Dokl. Acad. Nauk Ukr. S5R, 1 (1966) 38-41.