Related papers: On Relations among Fourier Coefficients and Sum-fu…
We consider the relations between well-known Fourier transform algorithms.
We prove several results related to the theorem of Logvinenko and Sereda on determining sets for functions with Fourier transforms supported in an interval. We obtain a polynomial instead of exponential bound in this theorem, and we extend…
We generalise the Fundamental Theorem of Calculus to higher dimensions. Our generalisation is based on the observation that the antiderivative of a function of $n$-variables is a solution of a partial differential equation of order $n$…
We define a Fourier transform and a convolution product for functions and distributions on Heisenberg--Clifford Lie supergroups. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for…
We describe an inequality of finite or infinite sequences of real numbers and their quotients. More precisely, we compare the quotient of H\"older functionals of two sequences of numbers with the sum of their quotients. In the last section…
We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…
In this short note, we derive an upper-bound for the sum of two comparison functions, namely for the sum of a class K and an extended class K function. To the best of our knowledge, the relations derived in this note have not been…
The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…
The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is…
We consider equations of the form Bf=g, where B is a Galois connection between lattices of functions. This includes the case where B is the Legendre-Fenchel transform, or more generally a Moreau conjugacy. We characterise the existence and…
The classical Liouville property says that all bounded harmonic functions in $\mathbb{R}^n$, i.e.\ all bounded functions satisfying $\Delta f = 0$, are constant. In this paper we obtain necessary and sufficient conditions on the symbol of a…
We study a duality for the $n$-point functions in VEV formalism that we call the ordinary vs fully simple duality. It provides an ultimate generalisation and a proper context for the duality between maps and fully simple maps observed by…
We translate Davenport's and Heilbronn's work on a quantitative version of the Oppenheim conjecture for indefinite diagonal quadratic forms in 5 variables into the setting of function fields.
Spivey presented a new approach to evaluate combinatorial sums by using finite differences. We present some closed forms for sums involving the binomial coefficients, Fibonacci and Lucas numbers in terms of the falling factorial.
We prove the following generalisation of Bohr theorem : let $K\subset\mathbb C$ a continuum, $(F_n)_n$ its Faber polynomials, $\Omega_R=\{\Phi_K<R\}, (R>1)$ the levels sets of the Green function; then there exists $R_0>1$ such that for any…
The lower and upper bounds are found for the leading term of summatory totient function $\sum_{k\leq N}k^u\phi^v(k)$ in various ranges of $u\in{\mathbb R}$ and $v\in{\mathbb Z}$.
In this note a general approach is suggested for comparison of operators. This is done by means of the Fourier transform of a measure. This approach is applied to comparison of approximation properties of various summability methods of the…
Lifting theorems are theorems that bound the communication complexity of a composed function $f\circ g^{n}$ in terms of the query complexity of $f$ and the communication complexity of $g$. Such theorems constitute a powerful generalization…
In this paper, we establish a general discrete Fourier restriction theorem. As an application, we make some progress on the discrete Fourier restriction associated with KdV equation.
The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems…