About Certain Singular Kernels $K(x,y) = K_1(x-y)K_2(x+y)$.

Certain Positive-definite Kernels

In one way or another, the extension of the standard Brownian motion process {B¡: t e [0,oo)} to a (Gaussian) random field {Bt: t € R+} involves a proof of the positive semi-definiteness of the kernel used to generalize p(s, 1) = cov(Bs,B¡) = s A t to multidimensional time. Simple direct analytical proofs are provided here for the cases of (i) the Levy multiparameter Brownian motion, (ii) the C...

An efficient algorithm for the evaluation of certain convolution integrals with singular kernels

In this short note, we are concerned with the evaluation of certain convolution integrals with singular kernels. The problem is as follows. Given a kernel function K(t) which is very often singular at the origin and a density function σ(t), evaluate C(t) = ∫ t 0 K(t − τ)σ(τ)dτ for t = ∆t, 2∆t, · · · , T = N∆t. We will oftern write C(tk) = C(k∆t) = Ck in short, and similarly for σ. Direct comput...

Szegö Kernels for Certain Unbounded Domains

Transcendental Lattices of Certain Singular K3 Surfaces

We present a method of Zariski-van Kampen type for the calculation of the transcendental lattice of a complex projective surface. As an application, we calculate the transcendental lattices of complex singular K3 surfaces associated with an arithmetic Zariski pair of maximizing sextics of type A10 + A9 that are defined over Q( √ 5) and are conjugate to each other by the action of Gal(Q( √ 5)/Q).

More about measures and Jacobians of singular random matrices

In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.