On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator

S. M. Bahri

Mathematica Bohemica (2012)

  • Volume: 137, Issue: 3, page 249-258
  • ISSN: 0862-7959

Abstract

top
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 , μ ) 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 .

How to cite

top

Bahri, S. M.. "On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator." Mathematica Bohemica 137.3 (2012): 249-258. <http://eudml.org/doc/246727>.

@article{Bahri2012,
abstract = {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 $A$.},
author = {Bahri, S. M.},
journal = {Mathematica Bohemica},
keywords = {defect indices; integral operator; quasi-selfadjoint extension; spectral theory; defect index; quasi-selfadjoint extension; spectrum; symmetric integral operator of Carleman type},
language = {eng},
number = {3},
pages = {249-258},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator},
url = {http://eudml.org/doc/246727},
volume = {137},
year = {2012},
}

TY - JOUR
AU - Bahri, S. M.
TI - On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator
JO - Mathematica Bohemica
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 137
IS - 3
SP - 249
EP - 258
AB - 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 $A$.
LA - eng
KW - defect indices; integral operator; quasi-selfadjoint extension; spectral theory; defect index; quasi-selfadjoint extension; spectrum; symmetric integral operator of Carleman type
UR - http://eudml.org/doc/246727
ER -

References

top
  1. Akhiezer, N. I., Glazman, I. M., Theory of Linear Operators in Hilbert Space, Dover, New York (1993). (1993) Zbl0874.47001MR1255973
  2. Aleksandrov, E. L., On the resolvents of symmetric operators which are not densely defined, Russian Izv. Vyssh. Uchebn. Zaved., Mat. 3-12 (1970). (1970) MR0287345
  3. Bahri, S. M., 10.4171/ZAA/1310, Z. Anal. Anwend. 26 57-64 (2007). (2007) Zbl1142.47027MR2306105DOI10.4171/ZAA/1310
  4. Bahri, S. M., Spectral properties of a certain class of Carleman operators, Arch. Math., Brno 43 163-175 (2007). (2007) Zbl1164.05037MR2354805
  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). (2008) Zbl1178.45019MR2505450
  6. Berezanskii, Yu. M., Expansions in Eigenfunctions of Selfadjoint Operators, Transl. Math. Monogr., 17, Amer. Math. Soc., Providence, RI (1968). (1968) Zbl0157.16601MR0222718
  7. Carleman, T., Sur les équations intégrales singuli ères à noyau réel et symétrique, Almquwist Wiksells Boktryckeri Uppsala (1923). (1923) 
  8. Gresztesy, F., Makarov, K., Tsekanovskii, E., 10.1006/jmaa.1998.5948, J. Math. Anal. Appl. 222 594-606 (1998). (1998) MR1628437DOI10.1006/jmaa.1998.5948
  9. Glazman, I. M., On a class of solutions of the classical moment problem, Zap. Khar'kov. Mat. Obehch 20 95-98 (1951). (1951) MR0049252
  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). (1955) MR0074636
  11. Gorbachuk, M. L., Gorbachuk, V. I., M. G. Krein's lectures on entire operators, Birkhäuser, Basel (1997). (1997) Zbl0883.47008MR1466698
  12. Allan, Gut, Probability: A graduate course, Springer, New York (2005). (2005) MR2125120
  13. Korotkov, V. B., Integral Operators, Russian Nauka, Novosibirsk (1983). (1983) Zbl0558.45013
  14. Kurasov, P., Kuroda, S. T., Krein's formula and perturbation theory, J. Oper. Theory 51 321-334 (2004). (2004) MR2074184
  15. Langer, H., Textorius, B., 10.2140/pjm.1977.72.135, Pacific J. Math. 72 135-165 (1977). (1977) Zbl0335.47014MR0463964DOI10.2140/pjm.1977.72.135
  16. Simon, B., Trace Ideals and Their Applications, 2nd edition, Amer. Math. Soc., Providence, RI (2005). (2005) MR2154153
  17. Shtraus, A. V., Extensions and generalized resolvents of a symmetric operator which is not densely defined, Russian Izv. Akad. Nauk SSSR, Ser. Mat. (1970), 175-202; Math. USSR, Izv. (1970), 179-208. Zbl0216.16403MR0278098
  18. Targonski, Gy. I., On Carleman integral operators, Proc. Amer. Math. Soc. 18 (1967),450-456. (1967) Zbl0147.12002MR0215139
  19. Weidman, J., 10.1007/BF01168477, Manuscripts Math. 1-38 (1970), 2. (1970) DOI10.1007/BF01168477
  20. Weidman, J., Linear operators in Hilbert spaces, Springer, New-York (1980). (1980) 

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.