Majorization for certain classes of meromorphic functions defined by integral operator

Here we investigate a majorization problem involving starlike meromorphic functions of complex order belonging to a certain subclass of meromorphic univalent functions defined by an integral operator introduced recently by Lashin

Majorization for Certain Classes of Analytic Multivalent Functions

In the present paper we investigate the majorization properties for certain classes of multivalent analytic functions defined by extended multiplier transformation. Moreover, we point out some new or known consequences of our main result

Majorization problem for certain class of p-valently analytic function defined by generalized fractional differintegral operator

AbstractIn this paper we investigate a majorization problem for a subclass of p-valently analytic function involving a generalized fractional differintegral operator. Some useful consequences of the main result are mentioned and relevance with some of the earlier results are also pointed out

Distance-based discriminant analysis method and its applications

This paper proposes a method of finding a discriminative linear transformation that enhances the data's degree of conformance to the compactness hypothesis and its inverse. The problem formulation relies on inter-observation distances only, which is shown to improve non-parametric and non-linear classifier performance on benchmark and real-world data sets. The proposed approach is suitable for both binary and multiple-category classification problems, and can be applied as a dimensionality reduction technique. In the latter case, the number of necessary discriminative dimensions can be determined exactly. Also considered is a kernel-based extension of the proposed discriminant analysis method which overcomes the linearity assumption of the sought discriminative transformation imposed by the initial formulation. This enhancement allows the proposed method to be applied to non-linear classification problems and has an additional benefit of being able to accommodate indefinite kernel

Gabor representations of evolution operators

We perform a time-frequency analysis of Fourier multipliers and, more generally, pseudodifferential operators with symbols of Gevrey, analytic and ultra-analytic regularity. As an application we show that Gabor frames, which provide optimally sparse decompositions for Schroedinger-type propagators, reveal to be an even more efficient tool for representing solutions to a wide class of evolution operators with constant coefficients, including weakly hyperbolic and parabolic-type operators. Besides the class of operators, the main novelty of the paper is the proof of super-exponential (as opposite to super-polynomial) off-diagonal decay for the Gabor matrix representation.Comment: 26 page

Asymptotic estimates for interpolation and constrained approximation in H2 by diagonalization of Toeplitz operators

Sharp convergence rates are provided for interpolation and approximation schemes in the Hardy space H-2 that use band-limited data. By means of new explicit formulae for the spectral decomposition of certain Toeplitz operators, sharp estimates for Carleman and Krein-Nudel'man approximation schemes are derived. In addition, pointwise convergence results are obtained. An illustrative example based on experimental data from a hyperfrequency filter is provided

(Uniform) convergence of twisted ergodic averages

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