About 76,700 results
|By finding an "integral representation," we mean the following: we are given a |
certain positive definite function ii, : SS ... Bochner's Theorem asserts that a
continuous function 4i : Rn — , C is a positive definite function on the group (R",+)
if and ...
|Perhaps the most spectacular convergence theorem involving positive |
functionals (in the guise of positive-definite ... functions on a locally compact
group converges to another continuous positive-definite function almost
everywhere if and only ...
|Conditions are sought under which a continuous positive-definite function on a |
closed subgroup is a restriction of such a function defined on the whole group.
This is found to be true for an arbitrary compact subgroup of a locally compact
|8 is based on a general theorem on positive definite operator-valued functions on |
a group. Definitions. Let G be a group. (i) A function T(s) on G, whose values are
boundedoperators on a Hilbert space H, is said to be positive definite if T(s−1) ...
|>(d) Let X be a group and hi, hi '□ X —y C positive definite functions. Show that |
hi + hi, othi and hi are also positive definite for any a > 0. (e) (i) Let X be a group,
Y a subgroup of X and h : Y —y C & positive definite function. Set hi(x) = h(x) if x ...
|5.7 NOTES AND REFERENCES Positive definite functions have applications in |
almost every area of modern analysis. In 1907 ... We mention just one more very
important area of their application: the theory of group representations. Let G be a
|In the present section we investigate positive definiteness on its own. In the main |
part of the book we deal with positive definite functions on the group Rd , but
occasionally we need also the group Zd. For this reason it is practical to treat the
|Representation of a topological group) I he spherical functions connected with |
unitarv representations of a locally compact group G are continuous positive-
definite functions on the group, and. conversely, any continuous positive-definite
|UNBOUNDED. POSITIVE. DEFINITE. FUNCTIONS. JAMES STEWART 1. |
Introduction. LetG be an abelian group, written additively. A complex- valued
function /, defined on G, is said to be positive definite if the inequality (1) Z f(st ~ si
)cjT, 2: 0 t ...