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Eigenvalues

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Full-Text Articles in Analysis

Eigenvalues And Approximation Numbers, Ryan Chakmak Jan 2019

Eigenvalues And Approximation Numbers, Ryan Chakmak

CMC Senior Theses

While the spectral theory of compact operators is known to many, knowledge regarding the relationship between eigenvalues and approximation numbers might be less known. By examining these numbers in tandem, one may develop a link between eigenvalues and l^p spaces. In this paper, we develop the background of this connection with in-depth examples.

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W1,P Regularity Of Eigenfunctions For The Mixed Problem With Nonhomogeneous Neumann Data, Kohei Miyazaki Jan 2018

W1,P Regularity Of Eigenfunctions For The Mixed Problem With Nonhomogeneous Neumann Data, Kohei Miyazaki

Murray State Theses and Dissertations

We consider an eigenvalue problem with a mixed boundary condition, where a second-order differential operator is given in divergence form and satisfies a uniform ellipticity condition. We show that if a function u in the Sobolev space W1,pD is a weak solution to the eigenvalue problem, then u also belongs to W1,pD for some p>2. To do so, we show a reverse Hölder inequality for the gradient of u. The decomposition of the boundary is assumed to be such that we get both Poincaré and Sobolev-type inequalities up to the boundary.

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Some Spectral Properties Of Hermitian Toeplitz Matrices, William Trench Jan 1994

Some Spectral Properties Of Hermitian Toeplitz Matrices, William Trench

William F. Trench

No abstract provided.

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Numerical Solution Of The Eigenvalue Problem For Hermitian Toeplitz Matrices, William Trench Jan 1989

Numerical Solution Of The Eigenvalue Problem For Hermitian Toeplitz Matrices, William Trench

William F. Trench

No abstract provided.

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Numerical Solution Of The Eigenvalue Problem For Symmetric Rationally Generated Toeplitz Matrices, William F. Trench Mar 1988

Numerical Solution Of The Eigenvalue Problem For Symmetric Rationally Generated Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.

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