Geometric Approximation of Point Interactions in Two-Dimensional Domains for Non-Self-Adjoint Operators

نویسندگان

چکیده

We define the notion of a point interaction for general non-self-adjoint elliptic operators in planar domains. show that such can be approximated geometric way by cutting out small cavity around point, at which is concentrated. On boundary cavity, we impose special Robin-type condition with nonlocal term. As shrinks to perturbed operator converges norm resolvent sense limiting one containing an arbitrary prescribed complex-valued coupling constant. The mentioned convergence holds few norms, and each these norms establish estimate rate. corollary convergence, prove spectrum.

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ژورنال

عنوان ژورنال: Mathematics

سال: 2023

ISSN: ['2227-7390']

DOI: https://doi.org/10.3390/math11040947