Eigenvalues and Completeness for Regular and Simply Irregular Two-point Differential Operators (Memoirs of the American Mathematical Society) - Softcover

Locker, John

 
9780821841716: Eigenvalues and Completeness for Regular and Simply Irregular Two-point Differential Operators (Memoirs of the American Mathematical Society)
Softcover
ISBN 10: 0821841718 ISBN 13: 9780821841716
Verlag: American Mathematical Society, 2008

Inhaltsangabe

In this monograph the author develops the spectral theory for an $n$th order two-point differential operator $L$ in the Hilbert space $L2[0,1]$, where $L$ is determined by an $n$th order formal differential operator $\ell$ having variable coefficients and by $n$ linearly independent boundary values $B 1, \ldots, B n$. Using the Birkhoff approximate solutions of the differential equation $(\rhon I - \ell)u = 0$, the differential operator $L$ is classified as belonging to one of three possible classes: regular, simply irregular, or degenerate irregular. For the regular and simply irregular classes, the author develops asymptotic expansions of solutions of the differential equation $(\rhon I - \ell)u = 0$, constructs the characteristic determinant and Green's function, characterizes the eigenvalues and the corresponding algebraic multiplicities and ascents, and shows that the generalized eigenfunctions of $L$ are complete in $L2[0,1]$. He also gives examples of degenerate irregular differential operators illustrating some of the unusual features of this class.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Reseña del editor

In this monograph the author develops the spectral theory for an $n$th order two-point differential operator $L$ in the Hilbert space $L2[0,1]$, where $L$ is determined by an $n$th order formal differential operator $\ell$ having variable coefficients and by $n$ linearly independent boundary values $B 1, \ldots, B n$. Using the Birkhoff approximate solutions of the differential equation $(\rhon I - \ell)u = 0$, the differential operator $L$ is classified as belonging to one of three possible classes: regular, simply irregular, or degenerate irregular. For the regular and simply irregular classes, the author develops asymptotic expansions of solutions of the differential equation $(\rhon I - \ell)u = 0$, constructs the characteristic determinant and Green's function, characterizes the eigenvalues and the corresponding algebraic multiplicities and ascents, and shows that the generalized eigenfunctions of $L$ are complete in $L2[0,1]$. He also gives examples of degenerate irregular differential operators illustrating some of the unusual features of this class.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
American Mathematical Society
Erscheinungsdatum
2008
Sprache
Englisch
ISBN 10 
0821841718
ISBN 13 
9780821841716
Einband
Tapa blanda
Anzahl der Seiten
177
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Verantwortliche Person
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