On the positive definiteness of a class of operators
β Scribed by Wu Ji-ke; Yuan Yong
- Publisher
- Springer
- Year
- 1987
- Tongue
- English
- Weight
- 159 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0253-4827
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
For a coinmutative senugoup (S, +, \*) with involution and a function f : S 4 [O, m), the set S ( f ) of those p 2 0 such that f\* is a positive definite function on S is a closed subsemigroup of [O, 00) containing 0. For S = (Hi, +, G\* = -G) it may happen that S(f) = { kd : k E No } for some d>O,a
Let \ be a nonnegative homogeneous function on R n . General structure of the set of numerical pairs ($, \*), for which the function (1&\ \* (x)) $ + is positive definite on R n is investigated; a criterion for positive definiteness of this function is given in terms of completely monotonic function
A problem of m-parameter perturbation of a family of positive definite operators with fvted bounds on their spectrum is considered. A criterion for m Q 2 and a sufficient condition for m > 2 are obtained for the operators of the perturbed family to be positive definite.