Title:
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On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator (English) |
Author:
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Bahri, S. M. |
Language:
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English |
Journal:
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Mathematica Bohemica |
ISSN:
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0862-7959 (print) |
ISSN:
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2464-7136 (online) |
Volume:
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137 |
Issue:
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3 |
Year:
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2012 |
Pages:
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249-258 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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In the present work, using a formula describing all scalar spectral functions of a Carleman operator $A$ of defect indices $( 1,1) $ in the Hilbert space $L^{2}( X,\mu ) $ that we obtained in a previous paper, we derive certain results concerning the localization of the spectrum of quasi-selfadjoint extensions of the operator $A$. (English) |
Keyword:
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defect indices |
Keyword:
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integral operator |
Keyword:
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quasi-selfadjoint extension |
Keyword:
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spectral theory |
MSC:
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45C05 |
MSC:
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45P05 |
MSC:
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47B25 |
MSC:
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58C40 |
idZBL:
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Zbl 1265.45001 |
idMR:
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MR3112486 |
DOI:
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10.21136/MB.2012.142892 |
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Date available:
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2012-08-19T21:14:02Z |
Last updated:
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2020-07-29 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/142892 |
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Reference:
|
[1] Akhiezer, N. I., Glazman, I. M.: Theory of Linear Operators in Hilbert Space.Dover, New York (1993). Zbl 0874.47001, MR 1255973 |
Reference:
|
[2] Aleksandrov, E. L.: On the resolvents of symmetric operators which are not densely defined.Russian Izv. Vyssh. Uchebn. Zaved., Mat. 3-12 (1970). MR 0287345 |
Reference:
|
[3] Bahri, S. M.: On the extension of a certain class of Carleman operators.Z. Anal. Anwend. 26 57-64 (2007). Zbl 1142.47027, MR 2306105, 10.4171/ZAA/1310 |
Reference:
|
[4] Bahri, S. M.: Spectral properties of a certain class of Carleman operators.Arch. Math., Brno 43 163-175 (2007). Zbl 1164.05037, MR 2354805 |
Reference:
|
[5] Bahri, S. M.: On convex hull of orthogonal scalar spectral functions of a Carleman operator.Bol. Soc. Parana. Mat. (3) 26 9-18 (2008). Zbl 1178.45019, MR 2505450 |
Reference:
|
[6] Berezanskii, Yu. M.: Expansions in Eigenfunctions of Selfadjoint Operators.Transl. Math. Monogr., 17, Amer. Math. Soc., Providence, RI (1968). Zbl 0157.16601, MR 0222718 |
Reference:
|
[7] Carleman, T.: Sur les équations intégrales singuli ères à noyau réel et symétrique.Almquwist Wiksells Boktryckeri Uppsala (1923). |
Reference:
|
[8] Gresztesy, F., Makarov, K., Tsekanovskii, E.: An addendum to Krein's formula.J. Math. Anal. Appl. 222 594-606 (1998). MR 1628437, 10.1006/jmaa.1998.5948 |
Reference:
|
[9] Glazman, I. M.: On a class of solutions of the classical moment problem.Zap. Khar'kov. Mat. Obehch 20 95-98 (1951). MR 0049252 |
Reference:
|
[10] Glazman, I. M., Naiman, P. B.: On the convex hull of orthogonal spectral functions.Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.] 102 445-448 (1955). MR 0074636 |
Reference:
|
[11] Gorbachuk, M. L., Gorbachuk, V. I.: M. G. Krein's lectures on entire operators.Birkhäuser, Basel (1997). Zbl 0883.47008, MR 1466698 |
Reference:
|
[12] Allan, Gut: Probability: A graduate course.Springer, New York (2005). MR 2125120 |
Reference:
|
[13] Korotkov, V. B.: Integral Operators.Russian Nauka, Novosibirsk (1983). Zbl 0558.45013 |
Reference:
|
[14] Kurasov, P., Kuroda, S. T.: Krein's formula and perturbation theory.J. Oper. Theory 51 321-334 (2004). MR 2074184 |
Reference:
|
[15] Langer, H., Textorius, B.: On generalized resolvents and Q-functions of symmetric linear relations (subspaces) in Hilbert space.Pacific J. Math. 72 135-165 (1977). Zbl 0335.47014, MR 0463964, 10.2140/pjm.1977.72.135 |
Reference:
|
[16] Simon, B.: Trace Ideals and Their Applications, 2nd edition.Amer. Math. Soc., Providence, RI (2005). MR 2154153 |
Reference:
|
[17] Shtraus, A. V.: Extensions and generalized resolvents of a symmetric operator which is not densely defined.Russian Izv. Akad. Nauk SSSR, Ser. Mat. {\it 34} (1970), 175-202; Math. USSR, Izv. {\it 4} (1970), 179-208. Zbl 0216.16403, MR 0278098 |
Reference:
|
[18] Targonski, Gy. I.: On Carleman integral operators.Proc. Amer. Math. Soc. 18 (1967),450-456. Zbl 0147.12002, MR 0215139 |
Reference:
|
[19] Weidman, J.: Carleman operators.Manuscripts Math. 1-38 (1970), 2. 10.1007/BF01168477 |
Reference:
|
[20] Weidman, J.: Linear operators in Hilbert spaces.Springer, New-York (1980). |
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