 About 76,700 results  books.google.com 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 ... 

 books.google.com 
 books.google.com Perhaps the most spectacular convergence theorem involving positive
functionals (in the guise of positivedefinite ... functions on a locally compact
group converges to another continuous positivedefinite function almost
everywhere if and only ... 

 books.google.com Conditions are sought under which a continuous positivedefinite 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
group ... 

 books.google.com 8 is based on a general theorem on positive definite operatorvalued 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) ... 

 books.google.com >(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 ... 

 books.google.com 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
... 

 books.google.com 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
... 

 books.google.com 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 positivedefinite
... 

 books.google.com 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 ... 

 