On One Class of Non-Dissipative Operators
DOI:
https://doi.org/10.15407/mag13.02.173Анотація
Вивчається недисипативний оператор iнтегрування у ваговому просторi. Доведено його подiбнiсть оператору iнтегрування в безваговому просторi. Отримано функцiональну модель для даного оператора.
Mathematics Subject Classification: 47A45.
Ключові слова:
недисипативний оператор, характеристична функція, подібність, функціональна модельПосилання
B.S. Pavlov, Basicity of an Exponential System and Muckenhoupt’s Condition. — Doklady Akademii Nauk SSSR, 247 (1979), No. 1, 37–40. (Russian)
S.V. Hruščev, N.K. Nikol’skii, and B. S. Pavlov, Unconditional Bases of Exponentials and of Reproducing Kernels. — Complex Analysis and Spectral Theory. Lectures Notes in Math. 864 (1981), 214–335.
G.M. Gubreev, Selected works. “Serednyak T. K.”, Dnepropetrovsk, 2014. (Russian)
G.M. Gubreev and V.N. Levchuk, Description of Unconditional Bases Formed by Values of the Dunkl Kernels. — Functional Analysis and Its Application 49 (2015), issue 1, 60–63.
R. Hatamleh and V.A. Zolotarev, On Model Representations of Non-Selfadjoint Operator with Infinitely Dimensional Imaginary Component. — J. Math. Phys., Anal., Geom. 11 (2015), No. 2, 174–186.
V.A. Zolotarev, Analytical Methods of Spectral Representations of Non-Selfadjoint and Non-Unitary Operators. Kharkiv National University Publishing House, MagPress, Kharkiv, 2003. (Russian)
I.C. Gohberg and M.G. Krein, Theory and Applications of Volterra Operators in Hilbert Space. Translations of Mathematical Monographs 24, 1970.
E. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill Book Company, Inc., 1955.
N.I. Akhiezer, Elements of the Theory of Elliptic Functions. American Mathematical Society, Providence, RI, 1990.
B.Ya. Levin, Lectures on Entire Functions. Transl. Math. Soc., Providence, RI, 1997.
L. de Branges, Hilbert Spaces of Entire Functions. Prentice Hall, London, 1968.
