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. …
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
31.15.12 $\rho(z)=\left(\prod_{j=1}^{N-1}\prod_{k=1}^{N}|z_{j}-a_{k}|^{\gamma_{k}-1}% \right)\left(\prod_{j
The normalized system of products (31.15.8) forms an orthonormal basis in the Hilbert space $L_{\rho}^{2}(Q)$. …
5: Bibliography S
• B. D. Sleeman (1978) Multiparameter spectral theory in Hilbert space. Research Notes in Mathematics, Vol. 22, Pitman (Advanced Publishing Program), Boston, Mass.-London.
• M. H. Stone (1990) Linear transformations in Hilbert space. American Mathematical Society Colloquium Publications, Vol. 15, American Mathematical Society, Providence, RI.
• 6: Bibliography D
• N. Dunford and J. T. Schwartz (1988) Linear operators. Part II. Wiley Classics Library, John Wiley & Sons, Inc., New York.
• 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 $\mathcal{H}$ 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
• A. M. Odlyzko (1987) On the distribution of spacings between zeros of the zeta function. Math. Comp. 48 (177), pp. 273–308.
• M. N. Olevskiĭ (1950) Triorthogonal systems in spaces of constant curvature in which the equation $\Delta_{2}u+\lambda u=0$ allows a complete separation of variables. Mat. Sbornik N.S. 27(69) (3), pp. 379–426 (Russian).
• S. Olver (2011) Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.
• A. M. Ostrowski (1973) Solution of Equations in Euclidean and Banach Spaces. Pure and Applied Mathematics, Vol. 9, Academic Press, New York-London.