Abstract
We find conditions under which the Kato inequality is preserved in the case where, instead of an operator with finitely many variables, an operator with infinitely many separated variables is taken. We use the inequality obtained to study both self-adjointness of the perturbed operator with infinitely many separated variables and the domain of definition of the form-sum of this operator and a singular potential.
This is a preview of subscription content, log in via an institution to check access.
References
Yu. M. Berezanskii,Self-Adjoint Operators in the Spaces of Functions of Infinitely Many Variables [in Russian]., Naukova Dumka (1978).
Yu. M. Berezanskii and V. G. Samoilenko, “Self-adjointness of differential operators with finitely or infinitely many variables and evolution equations,”Usp. Mat., Nauk,36, No. 5, 3–56 (1981).
M. Reed and B. Simon,Methods of Modern Mathematical Physics [Russian translation], Vol. 2, Mir, Moscow (1978).
Yu. G. Kondrat'ev, “Kato inequality for operators of second quantization,”Ukr. Mat. Zh.,35, No. 6, 735–736 (1973).
Yu. G. Kondrat'ev and T. V. Tsikalenko,Dirichlet Operators and Related Differential Equations [in Russian], Preprint No. 86.37, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1986).
Additional information
Kherson Pedagogic University, Kherson. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 5, pp. 718–720, May, 1999.
Rights and permissions
About this article
Cite this article
Samoilenko, V.G. Kato inequality for operators with infinitely many separated variables. Ukr Math J 51, 799–801 (1999). https://doi.org/10.1007/BF02591714
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02591714