Stochastic representation of fractional Bessel-Riesz motion

Bessel, Frame and Riesz Multipliers

Abstract. This paper introduces the concept of Bessel and frame multipliers. These operators are defined by a fixed pattern, called the symbol, which is used after analysis, before synthesis. This concept is a generalization of Gabor multipliers. It allows specialization to any analysis/synthesis systems, that form Bessel sequences, like e.g. wavelet frames. Basic properties of this general cla...

Brownian Sheet Images and Bessel–riesz Capacity

We show that the image of a 2–dimensional set under d–dimensional, 2–parameter Brownian sheet can have positive Lebesgue measure if and only if the set in question has positive (d/2)–dimensional Bessel–Riesz capacity. Our methods solve a problem of J.-P. Kahane.

Matrix Representation of Bounded Linear Operators By Bessel Sequences, Frames and Riesz Sequence

In this work we will investigate how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases as an extension of the known method of matrix representation by ONBs. We will give basic definitions of the functions connecting infinite matrices defining bounded operators on l and operators onH. We will show some structural results and give some...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Some Properties of Fractional Bessel Processes Driven by Fractional Brownian Motion

Fractional Bessel processes are defined and considering the processes associated with fractional Bessel processes 1 2 1 ), ( )) ( ( ) ( 0 < < = ∫ H t dB s B sign t X H t H H ) ( ) ( ) ( 1 0 s dB s R B t Y j H d