Related papers: A general explicit form for higher order approxima…
A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…
The paper presents new and known results on estimates of important linear and nonlinear approximation characteristics of generalized Wiener classes of functions of several variables in different metrics.
In this note we define a generalization of Hall-Littlewood symmetric functions using formal group law and give an elementary proof of the generating function formula for the generalized Hall-Littlewood symmetric functions. We also give some…
The recently developed theory of extended generating functions of symplectic maps are combined with methods to prove invertibility via high-order Taylor model methods to obtain rigorous lower bounds for the domains of definition of…
We generalize the concept of a number derivative, and examine one particular instance of a deformed number derivative for finite field elements. We find that the derivative is linear when the deformation is a Frobenius map and go on to…
We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…
Purpose of writing this paper is to solve a transcendental function containing a product of a variable and its double exponential by a unique method of approximation. If the value of the said product is given, then its inverse function is…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…
We analyze effective approximation of unitary matrices. In our formulation, a unitary matrix is represented as a product of rotations in two-dimensional subspaces, so-called Givens rotations. Instead of the quadratic dimension dependence…
When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes.…
The idea of generating integrals analogous to generating functions is first introduced in this paper. A new proof of the well-known Finite Harmonic Series Theorem in Analysis and Analytical Number Theory is then obtained by the method of…
We introduce a generating function associated to the homogeneous generators of a graded algebra that measures how far is this algebra from being finitely generated. For the case of some algebras of Frobenius endomorphisms we describe this…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
The exponential generating function of ordinary generating functions of diagonal sequences of general Sheffer triangles is computed by an application of Lagrange's theorem. For the special Jabotinsky type this is already known. An analogous…
Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…
Using notions of composita and composition of generating functions we obtain explicit formulas for Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, Associated Laguerre polynomials, Stirling polynomials, Abel polynomials,…
A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral…
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…