Existence of eigenvalues of operators acting in $L^2(R^n)$

V. S. Mokeychev

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We write out conditions that help to prove the existence of eigenvalues and characteristic values for operator $F(D)-C(\lambda): L^{2}(R^{m})\to L^{2}(R^{m})$, where $F(D)$ is a pseudodifferential operator with a symbol $F(i\xi)$ and $C(\lambda): L^{2}(R^{m}) \to L^{2}(R^{m})$ is a linear continuous operator.

Keywords: pseudodifferential operator, characteristic values, eigenvalues.

UDC: 517.956

Received: 09.02.2016

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:7, 25–34

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