Abstract
The aim of this work is to study the properties of the multi-component spectral problem generated by the linearized modified Stefan problem. On the basis of the abstract Green’s formula for a triple of Hilbert spaces, proved by N.Kopachevsky and S.Krein, an abstract generalization of the spectral problem is considered. Studying auxiliary abstract boundary value problems and properties of the corresponding operators, we prove that the spectrum consists of real normal eigenvalues and that the system of eigenelements forms an orthonormal basis in some Hilbert space.
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The paper is dedicated to brothers Mark and Selim Kreins
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Kopachevsky, N.D., Voytitsky, V.I. (2009). On the Modified Spectral Stefan Problem and Its Abstract Generalizations. In: Adamyan, V.M., et al. Modern Analysis and Applications. Operator Theory: Advances and Applications, vol 191. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9921-4_24
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DOI: https://doi.org/10.1007/978-3-7643-9921-4_24
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