Hilbert space
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10 matching pages
1: Brian D. Sleeman
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►He is author of the book Multiparameter spectral theory in Hilbert space, published by Pitman in 1978, and coauthor (with D.
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2: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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§1.18(i) Hilbert spaces
… ► … ►§1.18(iii) Linear Operators on a Hilbert Space
… ►Self-Adjoint and Symmetric Operators
… ►Formally Self-Adjoint and Self-Adjoint Differential Operators: Self-Adjoint Extensions
…3: 31.16 Mathematical Applications
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►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:
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4: 31.15 Stieltjes Polynomials
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31.15.12
►The normalized system of products (31.15.8) forms an orthonormal basis in the Hilbert space
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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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Linear transformations in Hilbert space.
American Mathematical Society Colloquium Publications, Vol. 15, American Mathematical Society, Providence, RI.
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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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7: 18.2 General Orthogonal Polynomials
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►A system of OP’s satisfying (18.2.1) and (18.2.5) is complete if each in the Hilbert space
can be approximated in Hilbert norm by finite sums .
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8: 18.39 Applications in the Physical Sciences
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►However, in the remainder of this section will will assume that the spectrum is discrete, and that the eigenfunctions of form a discrete, normed, and complete basis for a Hilbert space.
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9: 25.17 Physical Applications
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►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.
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►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).
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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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Triorthogonal systems in spaces of constant curvature in which the equation allows a complete separation of variables.
Mat. Sbornik N.S. 27(69) (3), pp. 379–426 (Russian).
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Numerical solution of Riemann-Hilbert problems: Painlevé II.
Found. Comput. Math. 11 (2), pp. 153–179.
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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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