ON AN APPLICATION OF PARSEVAL’S FORMULA TO PROBLEMS OF Gκ θ -SUMMABILITY OF EIGENFUNCTION EXPANSION OF THE LAPLACIAN OPERATOR | Zendy

Mirjana Vuković | Zendy; Emil Ilić-Georgijević | Zendy; O. STEVANOVIĆ | Zendy

Open Access

ON AN APPLICATION OF PARSEVAL’S FORMULA TO PROBLEMS OF Gκ θ -SUMMABILITY OF EIGENFUNCTION EXPANSION OF THE LAPLACIAN OPERATOR

Author(s) -

Mirjana Vuković,

Emil Ilić-Georgijević,

O. STEVANOVIĆ

Publication year - 2016

Publication title -

sarajevo journal of mathematics

Language(s) - English

Resource type - Journals

eISSN - 2233-1964

pISSN - 1840-0655

DOI - 10.5644/sjm.12.2.12

Subject(s) - mathematics , parseval's theorem , eigenfunction , laplace operator , operator (biology) , pure mathematics , algebra over a field , mathematical analysis , eigenvalues and eigenvectors , fourier transform , fourier analysis , biochemistry , physics , chemistry , repressor , quantum mechanics , transcription factor , fractional fourier transform , gene

In this paper, applying Parseval’s formula, we prove a Gθ – summability analogue of Avadhani’s theorem for the Riesz–summability of the eigenfunction expansion. A crucial step in our proof of this theorem was to find a function g(x) that would lead us to the kernel of the Gθ –summability, which is more complex than the kernel of the Riesz – summability.

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