In this paper we define a general integral operator for analytic functions in the open unit disk and we determine some conditions for univalence of this integral operator.

Four Fourier transforms are usually defined, the Integral Fourier transform, the Discrete-Time Fourier transform (DTFT), the Discrete Fourier transform (DFT) and the Integral Fourier transform for periodic functions. However, starting from their definitions, we show that all four Fourier transforms can be reduced to actually only one Fourier transform, the Fourier transform in the distributiona...

Let A(p) denote the class of functions which are analytic in the open unit disk U. By making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.

Motivated by the fact that twice Fourier transform plays role of parity operator. We systematically study integral transforms in case $\mathcal{PT}$-symmetric Hamiltonian. First, we obtain a closed analytical formula for exponential general Using Segal-Bargmann transform, investigate effect on eigenfunctions original As an immediate application, comment holomorphic representation non-Hermitian ...

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

We analyze a certain class of integral equations associated with Marchenko equations and Gel’fand-Levitan equations. Such integral equations arise through a Fourier transformation on various ordinary differential equations involving a spectral parameter. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution in terms of the unper...

Every completely positive map G that commutes which the Hamiltonian time evolution is an integral or sum over CP-maps Gσ where σ is the energy that is transferred to or taken from the environment. If the spectrum is non-degenerated each Gσ is an energy shift followed by a dephasing channel. The Kraus operator of the energy shift is a partial isometry which defines a translation on R with respec...