Fractal trigonometric approximation.
Fractional Korovkin Theory Based on Statistical Convergence
2000 Mathematics Subject Classification: 41A25, 41A36, 40G15.In this paper, we obtain some statistical Korovkin-type approximation theorems including fractional derivatives of functions. We also show that our new results are more applicable than the classical ones.
Fractional powers of operators, K-functionals, Ulyanov inequalities
Given an equibounded (₀)-semigroup of linear operators with generator A on a Banach space X, a functional calculus, due to L. Schwartz, is briefly sketched to explain fractional powers of A. Then the (modified) K-functional with respect to , α > 0, is characterized via the associated resolvent R(λ;A). Under the assumption that the resolvent satisfies a Nikolskii type inequality, , for a suitable Banach space Y, an Ulyanov inequality is derived. This will be of interest if one has good control...
Fractional Trigonometric Korovkin Theory in Statistical Sense
2000 Mathematics Subject Classification: 41A25, 41A36.In the present paper, we improve the classical trigonometric Korovkin theory by using the concept of statistical convergence from the summability theory and also by considering the fractional derivatives of functions. We also show that our new results are more applicable than the classical ones.
Frame Analysis of Irregular Periodic Sampling of Signals anf Their Derivatives.
Free-form surfaces for scattered data by neural networks.
From Continous to Discrete Weyl-Heisenberg Frames Through Sampling.
From multi-instantons to exact results
In these notes, conjectures about the exact semi-classical expansion of eigenvalues of hamiltonians corresponding to potentials with degenerate minima, are recalled. They were initially motivated by semi-classical calculations of quantum partition functions using a path integral representation and have later been proven to a large extent, using the theory of resurgent functions. They take the form of generalized Bohr--Sommerfeld quantization formulae. We explain here their...
From Taylor to quadratic Hermite-Padé polynomials.
Function approximation of Seidel aberrations by a neural network
This paper deals with the possibility of using a feedforward neural network to test the discrepancies between a real astronomical image and a predefined template. This task can be accomplished thanks to the capability of neural networks to solve a nonlinear approximation problem, i.e. to construct an hypersurface that approximates a given set of scattered data couples. Images are encoded associating each of them with some conveniently chosen statistical moments, evaluated along the axes; in this...
Functional characterization of best and good approximation in normed product spaces.
In [6], C. Dierick deals with a small but important collection of norms in the product of a finite number of normed linear spaces and he extends to such products some results on functional characterization of best approximations. In this paper we establish the widest scope in which the mentioned results remain valid.
Functions from -spaces and Taylor means
Functions of the form in
Fundamental quadratic splines and applications
Further Generalization of Kobayashi's Gamma Function
In this paper, we introduce a further generalization of the gamma function involving Gauss hypergeometric function 2F1 (a, b; c; z)