Eigenvalue-eigenfunction problem for Steklov's smoothing operator and differential-difference equations of mixed type

• Autorzy: Iakovlev S. I. , Iakovleva V.
• Języki publikacji: EN

Abstrakty

EN

It is shown that any μ ∈ C is an infinite multiplicity eigenvalue of the Steklov smoothing operator Sh acting on the space [formula]. For μ ≠ 0 the eigenvalue-eigenfunction problem leads to studying a differential-difference equation of mixed type. An existence and uniqueness theorem is proved for this equation. Further a transformation group is defined on a countably normed space of initial functions and the spectrum of the generator of this group is studied. Some possible generalizations are pointed out.

Słowa kluczowe

EN

Steklov's smoothing operator; spectrum; eigenvalues; eigenfunctions; mixed-type differential-difference equations; initial function; method of steps; countably normed space; transformation group; generator

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2013
• Tom: Vol. 33, no. 1
• Strony: 81--98
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Iakovlev S. I.

autor

Iakovleva V.

• Universidad Simon Bolivar, Departamento de Matematicas, Apartado Postal 89000 Caracas 1080-A, Venezuela,

Bibliografia

• [1] I. Gohberg, S. Goldberg, N. Krupnik, Traces and Determinants of Linear Operators, Birkhauser Verlag, Germany, 2000.
• [2] R.D. Driver, Ordinary and Delay Differential Eąuations, Applied Mathematical Sciences 20, Springer-Verlag, 1977.
• [3] J. Hale, Theory of Functional Differential Eąuations, Applied Mathematical Sciences 3, Springer-Verlag, 1977.
• [4] R. Bellman, K.L. Cooke, Differential-Difference Eąuations, A series of Monographs and Textbooks, Academic Press, 1963.
• [5] J. Weidmann, Linear Operators in Hilbert Spaces, Springer-Verlag, 1980.
• [6] I.M. Gelfand, G.E. Schilov, Generalized Functions, V.2, Academic Press, 1968.
• [7] K.J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Eąuations, Springer-Verlag, 2000.
• [8] S. Misohata, Theory of Eąuations with Partial Derivatives, Mir, Moscow, 1977.
• [9] K. Yosida, Functional Analysis, Springer-Verlag, 1965.