 About 33,300 results  books.google.com Apart from ^representations of involutive semigroups, our main objects of study
are operatorvalued positive definite functions. In this section, we assemble the
preliminaries concerning such functions, positive definite kernels, the associated
... 

 books.google.com 2.2.1 Positive Definite Kernels We start with some basic definitions and results.
As in the previous chapter, indices ;' and / are understood to run over 1, . . . , m.
Definition 2.3 (Gram Matrix) Given a function k : I2 > K (where K = C or K = W and
... 

 books.google.com This is done in the second section by a systematic application of positive definite
kernels on metric spaces. In the first section we present the basic definitions and
results on positive definite and on negative definite kernels and functions. 

 books.google.com cn = 0 then the matrix is called strictly positive definite. A positive definite kernel is
one that always produces a positive definite Gram matrix for elements in X. More
precisely: Definition 2.2.3 (Positive definite kernel) Iffor alln ∈ N andfor allx1 ,... 

 books.google.com Before discussing the consequences of Theorem 2.5, we give the missing
definitions of positive definite kernel and Hilbert space. Definition 2.5 (Positive
Definite Kernel Function). Let Xbea nonempty set. A function k : X×X→R is called
... 

 books.google.com Spectral translation Empirical kernel map classifier with good generalization
performances, an SVM tends only to ... (6.12) An obvious problem with this
operation is that the logarithm of a positive definite kernel is not a positive definite
kernel in ... 

 books.google.com (4) The family of all positive definite kernels on E×E makes a convex cone, which
is closed in the topology of pointwise convergence. (5) We assume that f : Rd →
R is a real entire function of the form f(x) = ∑ a∈Nd0 caxα for some d ∈ N, ... 

 books.google.com It is thus interesting to investigate whether in general kernel functions can be
defined as the minimum and/or maximum of a set of kernels. In this section we
investigate whether certain uses of minima and/or maxima give rise to positive
definite ... 

 books.google.com n∑ i=1 c i = 0, then N(·,·) is referred to as a negative definite kernel. If the equality
is reached only if ci = cj = 0 then the kernel is referred to as strongly negative
definite. Note that positive definite kernels are often referred to as Mercer kernels
... 

 books.google.com (ii) If {gen} is a sequence of positive definite functions and (,0n(£E) —> <p(x) for
all x, then 4,0 is positive definite. ... let K (x,y) be a bounded continuous complex
valued function on I X I. We say K is a positive definite kernel if /I Kay) f(w) M my 2
... 

 