Exact calculations of Feynman’s path integrals (defined on a time lattice) are mainly based on recurrence integral formulas in which the convolution of two functions having a common feature retains the same feature. Therefore, exactly soluble path integrals in quantum mechanics may be classified by their recurrence integral formula used in the calculation. According to this classification, ther...

In this paper we consider the modified Hadamard product or convolution of analytic functions with negative coefficients, combined with an Sǎlǎgean integral operator. We discuss when it is a given class. Following idea of U. Bednarz and J. Sokól we shall determine the order of convolution consistence for certain analytic functions with negative coefficients. AMS Subject Classification: 30C45, 30C50

In this paper, we will address the implementation of the Generalized Convolution Quadrature (GCQ) presented and analyzed in [M. LópezFernández, S. Sauter: A Generalized Convolution Quadrature with Variable Time Stepping, Preprint 17-2011, University of Zurich (2011)] for solving linear parabolic and hyperbolic evolution equations. Our main goal is to overcome the current restriction to uniform ...

Many concepts in computational flow visualization operate in the Lagrangian frame—they involve the integration of trajectories. A problem inherent to these approaches is the choice of an appropriate time length for the integration of these curves. While for some applications the choice of such a finite time length is straightforward, it represents in most other applications a parameter that nee...

We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates. It appears that one can compute the limits of all noncommutative moments (thus all spectral properties) of the random matrices we consider because, when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically fre...

Making use of a linear operator, which is defined here by means of the Hadamard product (or convolution), we introduce a class Qp(a, c;h) of analytic and multivalent functions in the open unit disk. An inclusion relation and a convolution property for the class Qp(a, c;h) are presented. Some integral-preserving properties are also given.

We introduce a class TS p(α) of analytic functions with negative coefficients defined by convolution with a fixed analytic function g(z) = z+ P∞ n=2 bnz , bn > 0, |z| < 1. We obtain the coefficient inequality, coefficient estimate, distortion theorem, a convolution result, extreme points and integral representation for functions in the class TS p(α).

In[6], Hu and Yang obtain a variant sharp estimate for the multilinear singular integral operators. The main purpose of this paper is to prove a sharp inequality for some multilinear operators related to certain non-convolution type integral operators. In fact, we shall establish the sharp inequality for the multilinear operators only under certain conditions on the size of the integral operato...

We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates. It appears that one can compute the limits of all non commutative moments (thus all spectral properties) of the random matrices we consider because, when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically fr...

The Fresnel sine integral S(x), the Fresnel cosine integral C(x), and the associated functions S + (x), S − (x), C + (x), and C − (x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel sine integral and its associated functions with x r + , x r are evaluated. 1. Introduction. The Fresnel integrals occur in the diffraction theory...