Related papers: Hankel transforms of general monotone functions

Chaundy and Jolliffe [4] proved that if $\{a_{n}\}$ is a non-increasing (monotonic) real sequence with $\lim\limits_{n\to \infty}a_{n}=0$, then a necessary and sufficient condition for the uniform convergence of the series…

We consider the Mellin transforms of certain generalized Hermite functions based upon certain generalized Hermite polynomials, characterized by a parameter $\mu>-1/2$. We show that the transforms have polynomial factors whose zeros lie all…

Let $\lambda$ denote the Liouville function. We show that for all sufficiently large integers $N$, the (non-trivial) convolution sum bound $$ \left|\sum_{1 \leq n < N} \lambda(n) \lambda(N-n)\right| < N-1 $$ holds. This (essentially)…

Let $[q] = \{0,1,\ldots,q-1\}$, let $\Delta[q]$ denote the simplex of probability measures on $[q]$, and let $\gamma$ denote the Lebesgue measure normalized on $\Delta[q]$. We prove that for any symmetric monotone function $f \colon[q]^n…

We generalize the previously given algebraic version of "Feynman's proof of Maxwell's equations" to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such…

Let $\Omega$ be an open and bounded subset of a Carnot Group $\mathbb{G}$ and $2\leq p<\infty$. In this paper we present some results related to the convergence of solutions of Dirichlet problems for sequences of monotone operators. The aim…

We extend our result on the convergence of double recurrence Wiener-Wintner averages to the case where we have a polynomial exponent. We will show that there exists a single set of full measure for which the averages \[ \frac{1}{N}…

In this paper we introduce a more general class of Foguel-Hankel operators, where the unilateral shift on $\ell^2(\mathbb{N}) $ is replaced by a general multiplication operator on the Hardy space $H^2$ . We prove that Peller's condition is…

It is well known that there are entire functions whose orbit approximates any other entire function under the action of a sequence of translation operators . This result also holds for an uncountable family of sequences of translation…

The aim of this paper is to prove a logarithmic and a Hirschman-Beckner entropic uncertainty principles for the Hankel wavelet transform. Then we derive a general form of Heisenberg-type uncertainty inequality for this transformation.

The Shapley-Folkman theorem shows that Minkowski averages of uniformly bounded sets tend to be convex when the number of terms in the sum becomes much larger than the ambient dimension. In optimization, Aubin and Ekeland [1976] show that…

We consider probability measures on the real line or unit circle with Jacobi or Verblunsky coefficients satisfying an $\ell^p$ condition and a generalized bounded variation condition. This latter condition requires that a sequence can be…

We show that for a nonnegative monotone sequence $\{c_k\}$ the condition $c_kk\to 0$ is sufficient for uniform convergence of the series $\sum_{k=1}^{\infty}c_k\sin k^{\alpha} x$ on any bounded set for $\alpha\in (0,2)$, and for an odd…

We study holomorphic functions attaining weighted norms and its connections with the classical theory of norm attaining holomorphic functions. We prove that there are polynomials on $\ell_p$ which attain their weighted but not their…

We extend the classical Lebesgue and Fubini differentiation theorems to functions of several variables, using the notions of joint derivative and joint monotonicity. Our first main result shows that for a function $f$ of bounded variation,…

We prove a sharp bound between sampling numbers and entropy numbers in the uniform norm for bounded convex sets of bounded functions.

We show that Newton's method converges globally at a linear rate for objective functions whose Hessians are stable. This class of problems includes many functions which are not strongly convex, such as logistic regression. Our linear…

The well-known Leibniz theorem (Leibniz Criterion or alternating series test) of convergence of alternating series is generalized for the case when the absolute value of terms of series are "not absolutely monotonously" convergent to zero.…

We show that strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are so that all solutions converge to a unique equilibrium. The result may be seen as a dual of a well-known…

We prove that convex functions of finite order on the real line and subharmonic functions of finite order on finite dimensional real space, bounded from above outside of some set of zero relative Lebesgue density, are bounded from above…