The exact spectral asymptotic of the logarithmic potential on harmonic function space | Zendy

Djordjije Vujadinović | Zendy

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The exact spectral asymptotic of the logarithmic potential on harmonic function space

Author(s) -

Djordjije Vujadinović

Publication year - 2019

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1906701v

Subject(s) - mathematics , logarithm , harmonic , mathematical analysis , eigenvalues and eigenvectors , operator (biology) , space (punctuation) , product (mathematics) , function (biology) , pure mathematics , geometry , physics , quantum mechanics , biochemistry , chemistry , linguistics , philosophy , repressor , biology , transcription factor , gene , evolutionary biology

In this paper we consider the product of the harmonic Bergman projection Ph: L2(D) ? L2h (D) and the operator of logarithmic potential type defined by L f(z)=- 1/2? ?D ln |z-?|f(?)dA(?), where D is the unit disc in C. We describe the asymptotic behaviour of the eigenvalues of the operator (PhL)+(PhL). More precisely, we prove that limn?+? n2sn(PhL) = ?4?2/3-1.

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