A generalized Hankel transformation on the spaces Fp,μ.
A generalized inversion formula for the continuous Jacobi transform.
A generalized Meijer transformation.
A Generalized Sampling Theorem with the Inverse of an Arbitrary Square Summable Sequence as Sampling Points.
A Green's function for a convertible bond using the Vasicek model.
A Hilbert transform for non-homogeneous martingales
A Laplace decomposition algorithm applied to a class of nonlinear differential equations.
A Laplace-like method for solving linear difference equations.
A limit theorem for the q-convolution
The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...
A mean value inequality for positive integral transformations with application to a maximal theorem
A method of inversion of the Laplace transform
A mixed norm estimate for the X-ray tranform.
A model for Toepliz operators in the space of entire functions of exponential type
A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics
The Linear Canonical Transform (LCT) is a four parameter class of integral transform which plays an important role in many fields of signal processing. Well-known transforms such as the Fourier Transform (FT), the FRactional Fourier Transform (FRFT), and the FreSnel Transform (FST) can be seen as special cases of the linear canonical transform. Many properties of the LCT are currently known but the extension of FRFTs and FTs still needs more attention. This paper presents a modified convolution...
A moment sequence in the q-world
The aim of the paper is to present some initial results about a possible generalization of moment sequences to a so-called q-calculus. A characterization of such a q-analogue in terms of appropriate positivity conditions is also investigated. Using the result due to Maserick and Szafraniec, we adapt a classical description of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity to the q-situation. This makes a link between q-positive definiteness and q-complete...
A multi-dimensional Hausdorff moment problems regularization by finite moments.
A necessary and sufficient condition for the representation of a function as a Hankel-Stieltjes transform
A new class of Bessel function integrals.
A new form of the spherical expansion of zonal functions and Fourier transforms of -finite functions.
A new of looking at distributional estimates; applications for the bilinear Hilbert transform.
Distributional estimates for the Carleson operator acting on characteristic functions of measurable sets of finite measure were obtained by Hunt. In this article we describe a simple method that yields such estimates for general operators acting on one or more functions. As an application we discuss how distributional estimates are obtained for the linear and bilinear Hilbert transform. These distributional estimates show that the square root of the bilinear Hilbert transform is exponentially lntegrable...