Abstract
We present conditions that allow us to prove the existence of eigenvalues and characteristic values for operator F(D) − C(λ): L 2(R m) → L 2(R m), where F(D) is a pseudo-differential operator with a symbol F(iξ) and C(λ): L 2(R m) → L 2(R m) is a linear continuous operator.
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Mokeichev, V. S. “Problem of Eigenvalues in the Whole Space for Equations With Discontinuous Coefficients”, Russian Mathematics 46, No. 6, 43–47 (2002).
Mokeichev V. S. “Absence of Eigenvalues in the Case of a Generalized Wave Conductor Problem”, Russian Mathematics 48, No. 6, 39–44 (2004) [in Russian].
Naimark, M. A. Linear Differential Operators (Nauka, Moscow, 1969) [in Russian].
Mokeichev, V. S. “Eigenvalues of Pseudo-Differential Operators”, in Modern Methods of the Theory of Boundary Value Problems: Materials of the Voronezh Spring Mathematical School “Pontryagin’s Readings–XXIV ”, Voronezh State University (Voronezh, 2013), P. 129 [in Russian].
Shubin, M. A. Pseudo-Differential Operators and Spectral Theory (Nauka, Moscow, 1978) [in Russian].
Mokeichev, V. S. “Existence and Basisness of Eigen and Adjoined Elements of Linear Operators”, Russian Mathematics 52, No. 6, 37–48 (2008).
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Original Russian Text © V.S. Mokeichev, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 7, pp. 30–40.
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Mokeichev, V.S. The existence of eigenvalues for operators acting in L 2(R n). Russ Math. 61, 25–34 (2017). https://doi.org/10.3103/S1066369X17070040
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DOI: https://doi.org/10.3103/S1066369X17070040