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This expository paper presents elementary proofs of four basic results concerning derivatives of quasi-convex functions. They are combined into a fifth theorem which is simple to apply and adequate in many cases. Along the way we establish…

In the first part of the paper the natural scheme for proving noncommutative individual ergodic theorems for multiple sequences is described and applied to obtain results on unrestricted convergence of multiaverages. In the second part…

The present article is devoted to the description of further investigations of the author of this article. These investigations (in terms of various representations of real numbers) include the generalized Salem functions and…

Self-similar symmetric $\alpha$-stable, $\alpha\in(0,2)$, mixed moving averages can be related to nonsingular flows. By using this relation and the structure of the underlying flows, one can decompose self-similar mixed moving averages into…

The main goal of the paper is to prove convergence in norm and pointwise almost everywhere on $L^p$, $p\in (1,\infty)$, for certain multiparameter polynomial ergodic averages in the spirit of Dunford and Zygmund for continuous flows. We…

We prove a stronger version of Jarden's Theorem for recurrence of powers of recursive functions

This note addresses the continuum problem, taking advantage of the breakthrough mentioned in the subtitle, and relating it to many recent advances occurring in set theory.

The main goal of this work is classifying the singularities of slice regular functions over a real alternative *-algebra A. This function theory has been introduced in 2011 as a higher-dimensional generalization of the classical theory of…

We consider weighted ergodic averages indexed by primes, where the weight depends on the prime, and is a "trace function" coming from algebraic geometry. We obtain extensions the classical mean-ergodic and pointwise ergodic theorems, as…

In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.

The purpose of this paper is to obtain some sufficient conditions to determine the relation between a meromorphic function and an L-function when certain differential polynomial generated by them sharing a one degree polynomial. The main…

Comment on ``Boosting Algorithms: Regularization, Prediction and Model Fitting'' [arXiv:0804.2752]

We prove that the main theorem for absolutely monotonic functions from the book Mitrinovi\'{c}~D.S., Pe\v{c}ari\'{c}~J.E., Fink~A.M. "Classical And New Inequalities In Analysis", Kluwer Academic Publishers, 1993, is not valid without…

In this paper, we first prove the strong Birkhoff Ergodic Theorem for subharmonic functions with the irrational shift on the Torus. Then, it is applied to the analytic quasi-periodic Jacobi cocycles. We show that if the Lyapunov exponent of…

The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of…

We study the long-time behavior of an additive functional that takes into account the jumps of a symmetric Markov process. This process is assumed to be observed through a biased observation scheme that includes the survival to events of…

I elaborate on the implementation of analyticity of hadronic quantities at the amplitude level and show that it amounts to the extension of Analytic Perturbation Theory of Shirkov and Solovtsov to non-integer (fractional) powers of the…

A brief presentation of basics of the theory of Tchebycheff and Markov systems of functions and its applications to extremal problems for integrals of such functions is given. The results, as well as all the necessary definitions, are…

We construct a generic extension in which the aleph_2 nd canonical function on aleph_1 exists.

We present a direct derivation of the theorem of M. Maxwell and M. Woodroofe (Ann. Probab. 28 (2000) 713-724), on martingale approximation of additive functionals of stationary Markov processes, from the non-reversible version of the…