Related papers: A Montel-type theorem for mixed differences
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
In the paper we formulate and verify a difference counterpart of the Macdonald-Mehta conjecture and its generalization for the Macdonald polynomials. Namely, we determine the Fourier transforms of the polynomials multiplied by the Gaussian,…
In this paper, we prove a generalization of the Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety over a number field. Our result improves and generalizes the previous…
We prove a quantitative version of the Polynomial Szemeredi Theorem for difference sets. This result is achieved by first establishing a higher dimensional analogue of a theorem of Sarkozy (the simplest non-trivial case of the Polynomial…
In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…
We prove a binomial formula for Macdonald polynomials and consider applications of it.
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…
We show how a commutative monad gives rise to a theory of extensive quantities, including (under suitable further conditions) a differential calculus of such. The relationship to Schwartz distributions is dicussed. The paper is a companion…
We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.
In this paper, the concept of the classical $f$-divergence (for a pair of measures) is extended to the mixed $f$-divergence (for multiple pairs of measures). The mixed $f$-divergence provides a way to measure the difference between multiple…
We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.
We prove a factorization theorem of generalized functions for moduli spaces of semistable parabolic bundles of any rank.
The main purpose of this work is to prove characterization theorems for generalized moment functions on groups. According one of the main results these are exponential polynomials that can be described with the aid of complete (exponential)…
Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular $j$ function. We show general cases in which these systems have solutions, and then we look at certain situations in…
In this paper, new classes of functions are defined. These spaces generalize Morrey spaces and give a refinement of Lebesgue spaces. Some embeddings between these new classes are also proved. Finally, the authors apply these classes of…
In this article, we prove a decomposition theorem on differential polynomials of theta functions of high level.
In this paper we prove the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane.
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
In this paper, the concept of the classical $f$-divergence for a pair of measures is extended to the mixed $f$-divergence for multiple pairs of measures. The mixed $f$-divergence provides a way to measure the difference between multiple…
In this note, a general formula is proved. It expresses the integral on the line of the product of a function $f$ and a periodic function $g$ in terms of the Fourier transform of $f$ and the Fourier coefficients of $g$. This allows the…