Schürmann’s theory of quantum Lévy processes, and more generally the theory of quantum stochastic convolution cocycles, is extended to the topological context of compact quantum groups and operator space coalgebras. Quantum stochastic convolution cocycles on a C-hyperbialgebra, which are Markov-regular, completely positive and contractive, are shown to satisfy coalgebraic quantum stochastic dif...

In this paper the problem of system equivalence is tackled for a rather general class of linear time-invariant systems. We consider AR-systems described by linear continuous shift-invariant operators with finite memory, acting on Frechet-signal spaces, containing the space £(lR) of infinitely differentiable functions on lR. This class is in one-one correspondence with matrices of suitable sizes...

We define new symbol classes for pseudodifferential operators and investigate their pseudodifferential calculus. The symbol classes are parametrized by commutative convolution algebras. To every solid convolution algebraA over a lattice Λ we associate a symbol class M. Then every operator with a symbol in M is almost diagonal with respect to special wave packets (coherent states or Gabor frames...

Let `p, 1 ≤ p ≤ ∞, be the space of all p-summable sequences and Ca be the convolution operator associated with a summable sequence a. It is known that the `pstability of the convolution operator Ca for different 1 ≤ p ≤ ∞ are equivalent to each other, i.e., if Ca has `p-stability for some 1 ≤ p ≤ ∞ then Ca has `q-stability for all 1 ≤ q ≤ ∞. In the study of spline approximation, wavelet analysi...

Abstract We consider a convolution-type operator on vector bundles over metric-measure spaces. This extends the analogous convolution Laplacian functions in our earlier work to bundles, and is natural extension of graph connection Laplacian. prove that for Euclidean or Hermitian connections closed Riemannian manifolds, spectrum this both approximate

Given a compactly supported function tp: W -*• C and the space 5 spanned by its integer translates, we study quasiinterpolants which reproduce (entirely or in part) the space H of all exponentials in S. We do this by imitating the action on H of the associated semi-discrete convolution operator *' by a convolution A*, A being a compactly supported distribution, and inverting A*|H by another ...

The goal of image deconvolution is to restore an image within a given area, from a blurred and noisy specimen. It is well known that the convolution operator integrates not only the image in the field of view of the given specimen, but also part of the scenery in the area bordering it. The result of a deconvolution algorithm which ignores the non-local properties of the convolution operator wil...

We develop a formalism to carry out coarse-grainings by using a timedependent projection operator in Heisenberg picture. A systematic perturbative expansion with respect to the interaction part of the Hamiltonian is given and the Langevin-type equation without a time-convolution integral term is obtained. This method is applied to a quantum field theoretical model and a coupled transport equati...

In this paper we consider the linear stochastic heat equation with additive noise in dimension one. Then, using the representation of its solution X as a stochastic convolution of the cylindrical Brownian motion with respect to an operator-valued kernel, we derive Itô’s and Tanaka’s type formulae associated to X.

We study the heat equation in n dimensional by Diamond Bessel operator. We find the solution by method of convolution and Fourier transform in distribution theory and also obtain an interesting kernel related to the spectrum and the kernel which is called Bessel heat kernel.