Generalized analytic and quasi-analytic vectors

• Autorzy: Rusinek J.
• Języki publikacji: EN

Abstrakty

EN

For every sequence (a[n]) of positive real numbers and an operator acting in a Banach space, we introduce the families of (a[n])-analytic and (a[n])-quasi-analytic vectors. We prove various properties of these families.

Słowa kluczowe

EN

analytic vector; essentially self-adjoint operator

PL

wektor analityczny; operator istotnie samosprzężony

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 1
• Strony: 39--46
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Rusinek J.

• Cardinal Stefan Wyszyński University, Faculty of Mathematics and Natural Sciences, College of Sciences, Dewajtis 5, 01-815 Warszawa, Poland,

Bibliografia

• [1] R. Beals, Semigroups and abstract Gevrey spaces, J. Funct. Anal. 10 (1972), 300-308.
• [2] M. Gevrey, Sur la nature analytique des solutions des équations aux dérivées partielles, Ann. Sci. École Norm. Sup. 35 (1918), 129-189.
• [3] V. I. Istrăţescu, Introduction to Linear Operator Theory, Dekker, New York, 1981.
• [4] E. Nelson, Analytic vectors, Ann. of Math. 70 (1959), 572-615.
• [5] A. E. Nussbaum, Quasi-analytic vectors, Ark. Mat. 6 (1965), 179-191.
• [6] -, A note on quasi-analytic vectors, Studia Math. 33 (1969), 305-309.
• [7] W. Rudin, Real and Complex Analysis, 2nd ed., McGraw-Hill, 1974.
• [8] J. Rusinek, p-Analytic and p-quasi-analytic vectors, Studia Math. 127 (1998), 233-250.
• [9] -, Non-linearity of the set of p-quasi-analytic vectors for some essentially self-adjoint operators, Bull. Polish Acad. Sci. Math. 48 (2000), 287-292.
• [10] B. Simon, The theory of semi-analytic vectors: A new proof of a theorem of Masson and McClary, Indiana Univ. Math. J. 20 (1970/71), 1145-1151.