symmetric operators

SearchAdvancedHelp

(0.001 seconds)

11—14 of 14 matching pages

11: Mathematical Introduction

… ►Other examples are: (a) the notation for the Ferrers functions—also known as associated Legendre functions on the cut—for which existing notations can easily be confused with those for other associated Legendre functions (§14.1); (b) the spherical Bessel functions for which existing notations are unsymmetric and inelegant (§§10.47(i) and 10.47(ii)); and (c) elliptic integrals for which both Legendre’s forms and the more recent symmetric forms are treated fully (Chapter 19). … ► ►►►►

$ℂ$	complex plane (excluding infinity).
…
$\mathrm{\Delta }$ (or ${\mathrm{\Delta }}_x$)	forward difference operator: $\mathrm{\Delta }f(x)=f(x+1)-f(x)$.
$\nabla$ (or ${\nabla }_x$)	backward difference operator: $\nabla f(x)=f(x)-f(x-1)$. (See also del operator in the Notations section.)
…

…

12: Bibliography R

… ►

Normal limit theorems for symmetric random matrices. Probab. Theory Related Fields 112 (3), pp. 411–423.

ⓘ

External Links:

ISSN 0178-8051, Document, MathReview (Alexei Khorunzhy), ZentralBlatt

Referenced by:

§35.9.

Encodings:

BibTeX

… ►

Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators. Academic Press, New York.

ⓘ

External Links:

ISBN 0-12-585004-2(vol.4), MathReview (P. R. Chernoff)

Referenced by:

§1.18(x).

Encodings:

BibTeX

… ►

On the computation of Lamé functions, of eigenvalues and eigenfunctions of some potential operators. Z. Angew. Math. Mech. 78 (1), pp. 66–72.

ⓘ

External Links:

ISSN 0044-2267, Document, MathReview Entry, ZentralBlatt

Referenced by:

§29.20(ii).

Encodings:

BibTeX

… ►

On the foundations of combinatorial theory. VIII. Finite operator calculus. J. Math. Anal. Appl. 42, pp. 684–760.

ⓘ

External Links:

ISSN 0022-247X, Document, Link, MathReview (P. Saphar), ZentralBlatt

Referenced by:

§18.2(xii).

Encodings:

BibTeX

… ►

On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media. In Differential Operators and Related Topics, Vol. I (Odessa, 1997), Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.

ⓘ

External Links:

ISBN 3-7643-6287-1, MathReview Entry, ZentralBlatt

Referenced by:

5th item.

Encodings:

BibTeX

…

13: 18.28 Askey–Wilson Class

… ► $y$) such that $P_n(z)=p_n(\frac{1}{2}(z+z^{-1}))$ in the Askey–Wilson case, and $P_n(y)=p_n(q^{-y}+c{q}^{y+1})$ in the $q$-Racah case, and both are eigenfunctions of a second order $q$-difference operator similar to (18.27.1). … ►The polynomials $p_n(x;a,b,c,d|q)$ are symmetric in the parameters $a,b,c,d$. … ►where the operator $L$ is defined by … ►In Tsujimoto et al. (2012) an extension of the Bannai–Ito polynomials occurs as eigenfunctions of a Dunkl type operator. …

14: 3.11 Approximation Techniques

… ►The matrix is symmetric and positive definite, but the system is ill-conditioned when $n$ is large because the lower rows of the matrix are approximately proportional to one another. … ►Since $X_{k\mathrm{\ell }}=X_{\mathrm{\ell }k}$, the matrix is again symmetric. … ►In consequence of this structure the number of operations can be reduced to $nm=n{\log }_{2}n$ operations. …