spectrum of an operator

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1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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Spectrum of an Operator

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2: 18.39 Applications in the Physical Sciences

… ►Also presented are the analytic solutions for the $L^2$, bound state, eigenfunctions and eigenvalues of the Morse oscillator which also has analytically known non-normalizable continuum eigenfunctions, thus providing an example of a mixed spectrum. … ►The spectrum is entirely discrete as in §1.18(v). … ►The spectrum is entirely discrete as in §1.18(v). ►An important, and perhaps unexpected, feature of the EOP’s is now pointed out by noting that for 1D Schrödinger operators, or equivalent Sturm-Liouville ODEs, having discrete spectra with $L^2$ eigenfunctions vanishing at the end points, in this case $\pm \mathrm{\infty }$ see Simon (2005c, Theorem 3.3, p. 35), such eigenfunctions satisfy the Sturm oscillation theorem. … ►The radial operator (18.39.28) …

3: 1.3 Determinants, Linear Operators, and Spectral Expansions

§1.3 Determinants, Linear Operators, and Spectral Expansions

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§1.3(iv) Matrices as Linear Operators

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Linear Operators in Finite Dimensional Vector Spaces

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Self-Adjoint Operators on ${𝐄}_n$

… ►The spectrum of such self-adjoint operators consists of their eigenvalues, ${\lambda }_i,i=1,2,\mathrm{\dots },n$, and all ${\lambda }_i\in ℝ$. …

4: Bibliography S

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An Introduction to the Operations with Series. 2nd edition, Chelsea Publishing Co., New York.

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Notes:

This is a reprint, with corrections, of the first edition [University of Pennsylvania Press, Philadelphia, Pa., 1924].

External Links:

MathReview, ZentralBlatt

Referenced by:

§24.1, §24.6.

Encodings:

BibTeX

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The Bound State of Weakly Coupled Schrödinger Operators in One and Two Dimensions. Annals of Physics 97 (2), pp. 279–288.

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External Links:

Document, MathReview Entry

Referenced by:

§1.18(viii).

Encodings:

BibTeX

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Operators with Singular Continuous Spectrum: I. General Operators. Annals of Mathematics 141 (1), pp. 131–145.

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External Links:

MathReview Entry

Referenced by:

§1.18(vii).

Encodings:

BibTeX

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An Introduction to Classical Electromagnetic Radiation. Cambridge University Press, Cambridge-New York.

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External Links:

ISBN 0-521-58093-5;0-521-58698-4

Referenced by:

§10.73(i).

Encodings:

BibTeX

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An Atlas of Functions. Hemisphere Pub. Corp., Washington.

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External Links:

ZentralBlatt

Referenced by:

§24.19(i), §25.18(i), §25.18(i).

Encodings:

BibTeX

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