Non-linearity of the set of p-quasi-analytic vectors for some essentially self-adjoint operators

• Autorzy: Rusinek, J.
• Języki publikacji: EN

Abstrakty

EN

We show that, for any p [is greater than or equal to] 1, there exists an essentially self-adjoint operator for which the set of p-quasi-analytic vectors is not linear.

Słowa kluczowe

PL

macierz Jakobiego; operator samosprzężony; teoria operatora; wektor quasi-analityczny

EN

Jacobi matrix; p-analytic vectors; self-adjoint operators

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 3
• Strony: 287--292
• Opis fizyczny: Bibliogr. 10 poz.,

Twórcy

autor

Rusinek, J.

• Institute of Applied Mathematics and Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland,

Bibliografia

• [1] P. R. Chernoff, Some remarks on quasi-analytic vectors, Trans. Amer. Math. Soc., 167 (1972) 105-113.
• [2] P. R. Chernoff, Quasi-analytic vectors and quasi-analytic functions, Bull. Amer. Math. Soc., 81 (1975) 637-646.
• [3] I. Ciorinescu, On quasi-analytic vectors for some classes of operators, in: Proceeding of the fourth conference on operator theory (Timisoara 1979), Tipografia Uni-versitalii, (1980) 214-226.
• [4] G. Constantin, V.I. Isträţescu, On quasi-analytic vectors for some classes of operators, Portugal Math., 42 (1983/84) 219-224.
• [5] A. El Koutri, Vecteurs a-quasi analytiques et semi-groupes analytiques, C. R. Acad. Sci. Paris Ser. I Math., 309 (1989) 767-769.
• [6] V. . Isträţescu, Introduction to linear operator theory, Marcel Dekker, New York 1981.
• [7] D. Masson, W. K. M c Clary, Classes of C' vectors and essential self-adjointness, J. Funct. Anal., 10 (1972) 19-32.
• [8] A. E. Nussbaum, Quasi-analytic vectors, Ark. Mat., 6 (1965) 179-191.
• [9] A. E. Nussbaum, A note on quasi-analytic vectors, Studia Math., 33 (1969) 305-309.
• [10] J. Rusinek, p-Analytic and p-quasi-analytic vectors, Studia Math., 127 (1998) 233-250.