Related papers: A simple proof of the generalized strong recurrenc…

In this note, we prove strong convergence of $q$-Gaussians with respect to a parameter $q$, which implies the spectrum of any self-adjoint non-commutative polynomial in $q$-Gaussians is continuously deformed with respect to $q$. With…

We consider a sequence of polynomials $\{P_n\}_{n \geq 0}$ satisfying a special $R_{II}$ type recurrence relation where the zeros of $P_n$ are simple and lie on the real line. It turns out that the polynomial $P_n$, for any $n \geq 2$, is…

An elementary analytic proof of the famous Riemann hypothesis is given. The main "accent" of the proof is a both using of the 2-dimensional double real and complex Laplace integral representations of the Green function $\mid z \mid^{-2}$.

We generalize the property that Riemann sums of a continuous function corresponding to equidistant subdivision of an interval converge to the integral of that function, and we give some applications of this generalization.

For each $f:[0,\infty)\to\Com$ formally consider its co-Poisson or M\"{u}ntz transform $g(x)=\sum_{n\geq 1}f(nx)-\frac{1}{x}\int_0^\infty f(t)dt$. For certain $f$'s with both $f, g \in L_2(0,\infty)$ it is true that the Riemann hypothesis…

We prove an abstract Nyquist criterion in a general set up. As applications, we recover various versions of the Nyquist criterion, some of which are new.

We will show that the sequences appearing in Bourgain's double recurrence result are good universal weights to the multiple recurrence averages with commuting measure-preserving transformations in norm. This will extend the pointwise…

The Riemann hypothesis, stating that the real part of all non-trivial zero points fo the zeta function must be $\frac{1}{2}$, is one of the most important unproven hypothesises in number theory. In this paper we will proof the Riemann…

This article presents a concise proof of the famous Benford's law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and…

We present a simple proof of the Riemann's Hypothesis (RH) where only undergraduate mathematics is needed.

After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…

For continuous maps of compact metric spaces $f:X\to X$ and $g:Y\to Y$ and for various notions of topological recurrence, we study the relationship between recurrence for $f$ and $g$ and recurrence for the product map $f\times g:X\times Y…

We give a short, self-contained, and elementary proof of the strong law of large numbers under a power law decay hypothesis for joint second moments. The result is related to the classical one by Lyons. However, we also provide a rate of…

In this paper, we consider sums of values of degenerate falling factorials and give a probabilistic proof of a recurrence relation for them. This may be viewed as a degenerate version of the recent probabilistic proofs on sums of powers of…

Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We…

Consider a system $(X, \mathcal{F}, \mu, T)$, bounded functions $f_1, f_2 \in L^\infty(\mu)$ and $a,b \in \ZZ.$ We show that there exists a set of full measure $X_{f_1, f_2}$ in $X$ such that for all $x \in X_{f_1, f_2}$ and for every…

Some considerations showing that renormalizable theories with consistent perturbative theries can not be nonperturbatively finite (in terms of bare parameters) are provided. Accordingly any fundamental unified theory has to be either non…

Leivant's ramified recurrence is one of the earliest examples of an implicit characterization of the polytime functions as a subalgebra of the primitive recursive functions. Leivant's result, however, is originally stated and proved only…

Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. It allows one to recover any element in any finite-dimensional subspace given finitely many of its samples with…

In this paper, we expand the theory of depth-unbiased source localization to unbiased parameter estimation and signal reconstruction of an arbitrary number of non-zero parameters to be recovered. The topic touches on the concept of exact…