# p-Analytic and p-quasi-analytic vectors

Studia Mathematica (1998)

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

## Access Full Article

top## Abstract

top## How to cite

topRusinek, 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

top- [Ch1] P. R. Chernoff, Some remarks on quasi-analytic vectors, Trans. Amer. Math. Soc. 167 (1972), 105-113. Zbl0259.47025
- [Ch2] P. R. Chernoff, Quasi-analytic vectors and quasi-analytic functions, Bull. Amer. Math. Soc. 81 (1975), 637-646. Zbl0304.47032
- [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
- [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. Zbl0691.47038
- [I] V. I. Istrăţescu, Introduction to Linear Operator Theory, Marcel Dekker, New York, 1981. Zbl0457.47001
- [K] K. Kuratowski, Introduction to Calculus, Pergamon Press, Oxford, 1969. Zbl0176.00501
- [MM] D. Masson and W. K. McClary, Classes of ${C}^{\infty}$ vectors and essential self-adjointness, J. Funct. Anal. 10 (1972), 19-32. Zbl0234.47026
- [N] E. Nelson, Analytic vectors, Ann. of Math. 70 (1959), 572-615. Zbl0091.10704
- [Nu1] A. E. Nussbaum, Quasi-analytic vectors, Ark. Mat. 6 (1965), 179-191. Zbl0182.46102
- [Nu2] A. E. Nussbaum, A note on quasi-analytic vectors, Studia Math. 33 (1969), 305-309. Zbl0189.43903
- [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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.