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1998 | 127 | 3 | 233-250
Tytuł artykułu

p-Analytic and p-quasi-analytic vectors

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EN
Abstrakty
EN
For every symmetric operator acting in a Hilbert space, we introduce the families of p-analytic and p-quasi-analytic vectors (p>0), indexed by positive numbers. We prove various properties of these families. We make use of these families to show that certain results guaranteeing essential selfadjointness of an operator with sufficiently large sets of quasi-analytic and Stieltjes vectors are optimal.
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autor
  • Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 00-913 Warszawa, Poland, rusinek@mimuw.edu.pl
  • Warsaw Higher School of Management for The Society of Economic Enterprise, Kawęczyńska 36, 03-772 Warszawa, Poland
Bibliografia
  • [Ch1] P. R. Chernoff, Some remarks on quasi-analytic vectors, Trans. Amer. Math. Soc. 167 (1972), 105-113.
  • [Ch2] P. R. Chernoff, Quasi-analytic vectors and quasi-analytic functions, Bull. Amer. Math. Soc. 81 (1975), 637-646.
  • [CoI] G. Constantin and V. I. Istrăţescu, On quasi-analytic vectors for some classes of operators, Portugal. Math. 42 (1983/84), 219-224.
  • [Ci] I. Ciorănescu, On quasi-analytic vectors for some classes of operators, in: Proceeding of the Fourth Conference on Operator Theory (Timişoara, 1979), Tipografia Universităţii, 1980, 214-226.
  • [E] A. El Koutri, Vecteurs α-quasi analytiques et semi-groupes analytiques, C. R. Acad. Sci. Paris Sér. I 309 (1989), 767-769.
  • [I] V. I. Istrăţescu, Introduction to Linear Operator Theory, Marcel Dekker, New York, 1981.
  • [K] K. Kuratowski, Introduction to Calculus, Pergamon Press, Oxford, 1969.
  • [MM] D. Masson and W. K. McClary, Classes of $C^∞$ vectors and essential self-adjointness, J. Funct. Anal. 10 (1972), 19-32.
  • [N] E. Nelson, Analytic vectors, Ann. of Math. 70 (1959), 572-615.
  • [Nu1] A. E. Nussbaum, Quasi-analytic vectors, Ark. Mat. 6 (1965), 179-191.
  • [Nu2] A. E. Nussbaum, A note on quasi-analytic vectors, Studia Math. 33 (1969), 305-309.
  • [S] 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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv127i3p233bwm
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