p-Analytic and p-quasi-analytic vectors

Jan Rusinek

Studia Mathematica (1998)

  • Volume: 127, Issue: 3, page 233-250
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Rusinek, Jan. "p-Analytic and p-quasi-analytic vectors." Studia Mathematica 127.3 (1998): 233-250. <http://eudml.org/doc/216470>.

@article{Rusinek1998,
abstract = {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.},
author = {Rusinek, Jan},
journal = {Studia Mathematica},
keywords = {symmetric operator; Hilbert space; -analytic and -quasi-analytic vectors; selfadjointness; Stieltjes vectors},
language = {eng},
number = {3},
pages = {233-250},
title = {p-Analytic and p-quasi-analytic vectors},
url = {http://eudml.org/doc/216470},
volume = {127},
year = {1998},
}

TY - JOUR
AU - Rusinek, Jan
TI - p-Analytic and p-quasi-analytic vectors
JO - Studia Mathematica
PY - 1998
VL - 127
IS - 3
SP - 233
EP - 250
AB - 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.
LA - eng
KW - symmetric operator; Hilbert space; -analytic and -quasi-analytic vectors; selfadjointness; Stieltjes vectors
UR - http://eudml.org/doc/216470
ER -

References

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  1. [Ch1] P. R. Chernoff, Some remarks on quasi-analytic vectors, Trans. Amer. Math. Soc. 167 (1972), 105-113. Zbl0259.47025
  2. [Ch2] P. R. Chernoff, Quasi-analytic vectors and quasi-analytic functions, Bull. Amer. Math. Soc. 81 (1975), 637-646. Zbl0304.47032
  3. [CoI] G. Constantin and V. I. Istrăţescu, On quasi-analytic vectors for some classes of operators, Portugal. Math. 42 (1983/84), 219-224. Zbl0564.47001
  4. [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. 
  5. [E] A. El Koutri, Vecteurs α-quasi analytiques et semi-groupes analytiques, C. R. Acad. Sci. Paris Sér. I 309 (1989), 767-769. Zbl0691.47038
  6. [I] V. I. Istrăţescu, Introduction to Linear Operator Theory, Marcel Dekker, New York, 1981. Zbl0457.47001
  7. [K] K. Kuratowski, Introduction to Calculus, Pergamon Press, Oxford, 1969. Zbl0176.00501
  8. [MM] D. Masson and W. K. McClary, Classes of C ∞ vectors and essential self-adjointness, J. Funct. Anal. 10 (1972), 19-32. Zbl0234.47026
  9. [N] E. Nelson, Analytic vectors, Ann. of Math. 70 (1959), 572-615. Zbl0091.10704
  10. [Nu1] A. E. Nussbaum, Quasi-analytic vectors, Ark. Mat. 6 (1965), 179-191. Zbl0182.46102
  11. [Nu2] A. E. Nussbaum, A note on quasi-analytic vectors, Studia Math. 33 (1969), 305-309. Zbl0189.43903
  12. [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. Zbl0244.47022

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