spectral problems

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1: 31.17 Physical Applications

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§31.17(i) Addition of Three Quantum Spins

… ►Consider the following spectral problem on the sphere $S_2$: ${𝐱}^2=x_s^2+x_t^2+x_u^2=R^2$. … ►For applications of Heun’s equation and functions in astrophysics see Debosscher (1998) where different spectral problems for Heun’s equation are also considered. …

2: Hans Volkmer

… ►Volkmer has published numerous papers on special functions, spectral theory, differential equations, and mathematical statistics. His book Multiparameter Eigenvalue Problems and Expansion Theorems was published by Springer as Lecture Notes in Mathematics No. …

3: 18.39 Applications in the Physical Sciences

… ►Shizgal (2015) gives a broad overview of techniques and applications of spectral and pseudo-spectral methods to problems arising in theoretical chemistry, chemical kinetics, transport theory, and astrophysics. …

4: Brian D. Sleeman

… ► thesis was Some Boundary Value Problems Associated with the Heun Equation. ►Sleeman published numerous papers in applied analysis, multiparameter spectral theory, direct and inverse scattering theory, and mathematical medicine. He is author of the book Multiparameter spectral theory in Hilbert space, published by Pitman in 1978, and coauthor (with D. …

5: Bibliography H

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Two Parametric Eigenvalue Problems of Differential Equations. In Spectral Theory of Differential Operators (Birmingham, AL, 1981), North-Holland Math. Stud., Vol. 55, pp. 233–241.

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External Links:

MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§28.7.

Encodings:

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6: 30.14 Wave Equation in Oblate Spheroidal Coordinates

… ►Equation (30.13.7) for $\xi \le {\xi }_0$ together with the boundary condition $w=0$ on the ellipsoid given by $\xi ={\xi }_0$, poses an eigenvalue problem with ${\kappa }^2$ as spectral parameter. …

7: William P. Reinhardt

… ►Older work on the scattering theory of the atomic Coulomb problem led to the discovery of new classes of orthogonal polynomials relating to the spectral theory of Schrödinger operators, and new uses of old ones: this work was strongly motivated by his original ownership of a 1964 hard copy printing of the original AMS 55 NBS Handbook of Mathematical Functions. …

8: 30.13 Wave Equation in Prolate Spheroidal Coordinates

… ►Equation (30.13.7) for $\xi \le {\xi }_0$, and subject to the boundary condition $w=0$ on the ellipsoid given by $\xi ={\xi }_0$, poses an eigenvalue problem with ${\kappa }^2$ as spectral parameter. …

9: Bibliography S

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Spectral Methods in Chemistry and Physics. Applications to Kinetic Theory and Quantum Mechanics. Scientific Computation, Springer-Verlag, Dordrecht.

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External Links:

ISBN 978-94-017-9453-4; 978-94-017-9454-1, Document, Link, MathReview (Gabriel Stoltz)

Referenced by:

§18.38(i), §18.39(iii), §18.39(iii), §18.39(iii).

Encodings:

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Orthogonal Polynomials on the Unit Circle. Part 2: Spectral Theory. American Mathematical Society Colloquium Publications, Vol. 54, American Mathematical Society, Providence, RI.

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External Links:

ISBN 0-8218-3675-7, MathReview (P. L. Duren), ZentralBlatt

Referenced by:

§18.33(i), §18.33(vi).

Encodings:

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Szegő’s Theorem and Its Descendants. Spectral Theory for $L^2$ Perturbations of Orthogonal Polynomials. M. B. Porter Lectures, Princeton University Press, Princeton, NJ.

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External Links:

ISBN 978-0-691-14704-8, MathReview (Harry Dym)

Referenced by:

§18.2(xi).

Encodings:

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Multiparameter spectral theory in Hilbert space. Research Notes in Mathematics, Vol. 22, Pitman (Advanced Publishing Program), Boston, Mass.-London.

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External Links:

ISBN 0-8224-8414-5, MathReview (F. H. Szafraniec), ZentralBlatt

Referenced by:

Profile Brian D. Sleeman.

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Mixed Boundary Value Problems in Potential Theory. North-Holland Publishing Co., Amsterdam.

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External Links:

MathReview (R. Shail), ZentralBlatt

Referenced by:

§10.22(iv).

Encodings:

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10: Bibliography G

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Quasirandom distributed bases for bound problems. J. Chem. Phys. 114 (9), pp. 3929–3939.

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Referenced by:

§18.39(iii).

Encodings:

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Problem 72-21, Laplace transforms of Airy functions. SIAM Rev. 15 (4), pp. 796–798.

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Notes:

Problem proposed by P. Smith.

External Links:

Document

Referenced by:

(9.10.14), (9.10.15), (9.10.16), §9.10(v).

Encodings:

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Numerical Analysis of Spectral Methods: Theory and Applications. Society for Industrial and Applied Mathematics, Philadelphia, PA.

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Notes:

CBMS-NSF Regional Conference Series in Applied Mathematics, No. 26

External Links:

MathReview (O. Widlund), ZentralBlatt

Referenced by:

§18.38(i).

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Stirling number representation problems. Proc. Amer. Math. Soc. 11 (3), pp. 447–451.

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External Links:

FullText, MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§26.1, §26.1, Notations S, Notations S.

Encodings:

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Spectral Methods and Their Applications. World Scientific Publishing Co. Inc., River Edge, NJ-Singapore.

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External Links:

ISBN 981-02-3333-7, MathReview (K. Moszyński), ZentralBlatt

Referenced by:

§18.38(i).

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