We consider perturbation by a slender potential of operators associated with sectorial sesquilinear forms. The potential depends on two small parameters one of which corresponds to the support length, whereas the inverse of the second parameter is the maximal value of the potential. It is shown that if the ratio of these two parameters tends to zero, then the perturbed operator weakly converges to the operator associated with the original sesquilinear form without slender potential. Bibliography: 14 titles.
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Translated from Problemy Matematicheskogo Analiza 75, April 2014, pp. 21–26.
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Bikmetov, A.R., Gadyl’shin, T.R. & Khusnullin, I.K. Perturbation by Slender Potential of Operators Associated with Sectorial Forms. J Math Sci 198, 677–683 (2014). https://doi.org/10.1007/s10958-014-1818-y
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DOI: https://doi.org/10.1007/s10958-014-1818-y