𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Magnetostatic Integral Operator for Ellipsoids

✍ Scribed by Stefan Ritter

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
190 KB
Volume
207
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

The magnetostatic integral operator in ‫ޒ‬ 3 is of considerable interest in both scattering and potential theory. As well as for its scalar pendant, the electrostatic integral operator, its eigenvalues, and its eigenfunctions play a fundamental role in the theory of permanent magnetization. While the eigenvalues of both operators are closely related, explicit expressions for the eigenfunctions of the magnetostatic operator are known only in the case when the underlying surface is a sphere. For the cases of ellipsoids and spheroids, we present explicit expressions for the eigenvalues in terms of Lame functions and associated Legendre functions and Γ©xpressions for eigenfunctions in terms of surface ellipsoidal and surface spheroidal harmonics, respectively. As an application the permanent magnetization of ellipsoids is discussed.

πŸ“œ SIMILAR VOLUMES

On Partial Sums of the Libera Integral O
On Partial Sums of the Libera Integral Operator
✍ Li Jian-Lin; Shigeyoshi Owa πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 151 KB

Let S be the class of functions f z which are analytic and univalent in the open Ε½ . X Ε½ . unit disk U with f 0 s 0 and f 0 s 1. The nth partial sums of the Libera Ε½ . Ε½ . Ε½ . integral operator F z for f z g S are denoted by S z, F . In the present paper, n Ε½ . the starlikeness property of S z, F i

Integral Operators on the Product of C(K
Integral Operators on the Product of C(K) Spaces
✍ Fernando Bombal; Ignacio Villanueva πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 131 KB

We study and characterize the integral multilinear operators on a product of C K spaces in terms of the representing polymeasure of the operator. Some applications are given. In particular, we characterize the Borel polymeasures that can be extended to a measure in the product Οƒ-algebra, generalizin