Hilbert space

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1: Brian D. Sleeman

… ►He is author of the book Multiparameter spectral theory in Hilbert space, published by Pitman in 1978, and coauthor (with D. …

2: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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§1.18(i) Hilbert spaces

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§1.18(iii) Linear Operators on a Hilbert Space

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Self-Adjoint and Symmetric Operators

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Formally Self-Adjoint and Self-Adjoint Differential Operators: Self-Adjoint Extensions

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3: 31.16 Mathematical Applications

… ►Expansions of Heun polynomial products in terms of Jacobi polynomial (§18.3) products are derived in Kalnins and Miller (1991a, b, 1993) from the viewpoint of interrelation between two bases in a Hilbert space: … ►

4: 31.15 Stieltjes Polynomials

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31.15.12

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Defines:

$\rho (z)$: weight function (locally)

Symbols:

$z$: complex variable, $\gamma$: real or complex parameter, $j$: nonnegative integer, $a$: complex parameter and $N+1$: number of singularities

Permalink:

http://dlmf.nist.gov/31.15.E12

Encodings:

pMML, png, TeX

See also:

Annotations for §31.15(iii), §31.15 and Ch.31

►The normalized system of products (31.15.8) forms an orthonormal basis in the Hilbert space $L_{\rho }^2(Q)$. …

5: Bibliography S

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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.

Encodings:

BibTeX

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Linear transformations in Hilbert space. American Mathematical Society Colloquium Publications, Vol. 15, American Mathematical Society, Providence, RI.

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Notes:

Reprint of the 1932 original

External Links:

ISBN 0-8218-1015-4, Document, Link, MathReview (P. R. Halmos)

Referenced by:

§1.18(x).

Encodings:

BibTeX

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6: Bibliography D

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Linear operators. Part II. Wiley Classics Library, John Wiley & Sons, Inc., New York.

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Notes:

Spectral theory. Selfadjoint operators in Hilbert space, With the assistance of William G. Bade and Robert G. Bartle, Reprint of the 1963 original, A Wiley-Interscience Publication

External Links:

ISBN 0-471-60847-5, MathReview Entry

Referenced by:

(1.18.68), §1.18(ix), §1.18(ix), §1.18(ix), §1.18(x).

Encodings:

BibTeX

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7: 18.2 General Orthogonal Polynomials

… ►A system $\{p_n(x)\}$ of OP’s satisfying (18.2.1) and (18.2.5) is complete if each $f(x)$ in the Hilbert space $L_w^2((a,b))$ can be approximated in Hilbert norm by finite sums ${\sum }_n{\lambda }_n{p}_n(x)$. …

8: 18.39 Applications in the Physical Sciences

… ►However, in the remainder of this section will will assume that the spectrum is discrete, and that the eigenfunctions of $\mathscr{H}$ form a discrete, normed, and complete basis for a Hilbert space. …

9: 25.17 Physical Applications

… ►This relates to a suggestion of Hilbert and Pólya that the zeros are eigenvalues of some operator, and the Riemann hypothesis is true if that operator is Hermitian. … ►Quantum field theory often encounters formally divergent sums that need to be evaluated by a process of regularization: for example, the energy of the electromagnetic vacuum in a confined space (Casimir–Polder effect). …

10: Bibliography O

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On the distribution of spacings between zeros of the zeta function. Math. Comp. 48 (177), pp. 273–308.

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External Links:

ISSN 0025-5718, FullText, Author’s Website, MathReview (S. L. Segal), ZentralBlatt

Referenced by:

§25.18(ii).

Encodings:

BibTeX

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Triorthogonal systems in spaces of constant curvature in which the equation ${\mathrm{\Delta }}_{2}u+\lambda u=0$ allows a complete separation of variables. Mat. Sbornik N.S. 27(69) (3), pp. 379–426 (Russian).

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Notes:

In Russian.

External Links:

MathReview (H. Busemann), ZentralBlatt

Referenced by:

§31.17(i).

Encodings:

BibTeX

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Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.

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External Links:

ISSN 1615-3375, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§32.17, §32.17.

Encodings:

BibTeX

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Solution of Equations in Euclidean and Banach Spaces. Pure and Applied Mathematics, Vol. 9, Academic Press, New York-London.

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Notes:

Third edition of Solution of equations and systems of equations

External Links:

MathReview (J. Burlak), ZentralBlatt

Referenced by:

§3.3(v), §3.8(iii).

Encodings:

BibTeX

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