Open AccessThe 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.