On the eigenvalues of certain canonical higher-order ordinary differential operators
Copyright policy )On the eigenvalues of certain canonical higher-order ordinary differential operators
We consider the operator of taking the $2p$th derivative of a function with zero boundary conditions for the function and its first $p-1$ derivatives at two distinct points. Our main result provides an asymptotic formula for the eigenvalues and resolves a question on the appearance of certain regular numbers in the eigenvalue sequences for $p=1$ and $p=3$.
LaTeX, 12 pages, 2 figures
- University of California United States
- University of California United States
- University of California, Santa Cruz United States
- University of California, San Francisco United States
- Chemnitz University of Technology Germany
ordinary differential operator, asymptotic expansion, Applied Mathematics, Eigenvalue, Asymptotic expansion, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Functional Analysis (math.FA), Mathematics - Functional Analysis, Sturm-Liouville theory, Primary 34L15, Secondary 15A15, 41A80, 47B15, Mathematics - Classical Analysis and ODEs, Ordinary differential operator, Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators, Classical Analysis and ODEs (math.CA), FOS: Mathematics, eigenvalue, Analysis
ordinary differential operator, asymptotic expansion, Applied Mathematics, Eigenvalue, Asymptotic expansion, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Functional Analysis (math.FA), Mathematics - Functional Analysis, Sturm-Liouville theory, Primary 34L15, Secondary 15A15, 41A80, 47B15, Mathematics - Classical Analysis and ODEs, Ordinary differential operator, Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators, Classical Analysis and ODEs (math.CA), FOS: Mathematics, eigenvalue, Analysis
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