![](/images/graphics-bg.png)
Green's Function and Convergence of Fourier Series for Elliptic Differential Operators with Potential from Kato Space
Author
Source
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-03-02
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
We consider the Friedrichs self-adjoint extension for a differential operator A of the form A=A0+q(x)⋅, which is defined on a bounded domain Ω⊂ℝn, n≥1 (for n=1 we assume that Ω=(a,b) is a finite interval).
Here A0=A0(x,D) is a formally self-adjoint and a uniformly elliptic differential operator of order 2m with bounded smooth coefficients and a potential q(x) is a real-valued integrable function satisfying the generalized Kato condition.
Under these assumptions for the coefficients of A and for positive λ large enough we obtain the existence of Green's function for the operator A+λI and its estimates up to the boundary of Ω.
These estimates allow us to prove the absolute and uniform convergence up to the boundary of Ω of Fourier series in eigenfunctions of this operator.
In particular, these results can be applied for the basis of the Fourier method which is usually used in practice for solving some equations of mathematical physics.
American Psychological Association (APA)
Serov, Valery. 2010. Green's Function and Convergence of Fourier Series for Elliptic Differential Operators with Potential from Kato Space. Abstract and Applied Analysis،Vol. 2010, no. 2010, pp.1-18.
https://search.emarefa.net/detail/BIM-506657
Modern Language Association (MLA)
Serov, Valery. Green's Function and Convergence of Fourier Series for Elliptic Differential Operators with Potential from Kato Space. Abstract and Applied Analysis No. 2010 (2010), pp.1-18.
https://search.emarefa.net/detail/BIM-506657
American Medical Association (AMA)
Serov, Valery. Green's Function and Convergence of Fourier Series for Elliptic Differential Operators with Potential from Kato Space. Abstract and Applied Analysis. 2010. Vol. 2010, no. 2010, pp.1-18.
https://search.emarefa.net/detail/BIM-506657
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-506657