Related papers: New monotone measure-based integrals inspired by s…
We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we…
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
In this expository paper aimed at a general mathematical audience, we discuss how to combine certain classic theorems of set-theoretic inner model theory and effective descriptive set theory with work on Hilbert's tenth problem and…
The problem of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure is discussed in the paper. The above problem is studied for elements of finite…
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
The main aim of this paper is to study the functional inequality \begin{equation*} \int_{[0,1]}f\bigl((1-t)x+ty\bigr)d\mu(t)\geq 0, \qquad x,y\in I \mbox{ with } x<y, \end{equation*} for a continuous unknown function $f:I\to{\mathbb R}$,…
The maximum of the modulus of a meromorphic function cannot be restricted from above by the Nevanlinna characteristic of this meromorphic function. But integrals from the logarithm of the module of a meromorphic function allow similar…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
In this paper we provide sufficient conditions that ensure the monotonicity, respectively the global injectivity of an operator. Further, some new analytical conditions that assure the injectivity/univalence of a complex function of one…
This paper explores generalized slice monogenic functions by introducing their operator symbols, representation formula, and integral formula. The study extends the Teodorescu transform to a broader class of theorems and inferences,…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
This paper focuses on various decompositions of topological measures, deficient topological measures, signed topological measures, and signed deficient topological measures. These set functions generalize measures and correspond to certain…
One considers Hilbert space valued measures on the Borel sets of a compact metric space. A natural numerical valued integral of vector valued continuous functions with respect to vector valued functions is defined. Using this integral,…
Analogy with Bayesian inference is used to formulate constraints within a scheme for functional integration proposed by Cartier and DeWitt-Morette. According to the analogy, functional counterparts of conditional and conjugate probability…
Robins et al. (2008, 2017) applied the theory of higher order influence functions (HOIFs) to derive an estimator of the mean $\psi$ of an outcome Y in a missing data model with Y missing at random conditional on a vector X of continuous…
We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals. The Fourier integral theorem, derived as a combination of a transform and inverse transform, arises as a special case. The…
In this article our main object of investigation is the simple modular density ideals $\mathcal{Z}_g(f)$ introduced in [Bose et al., Indag. math., 2018] where $g$ is a weight function, more precisely, $g\in G$, $G=\{g:\omega \to…
The monotone rearrrangement algorithm was introduced by Hardy, Littlewood and P\'olya as a sorting device for functions. Assuming that $x$ is a monotone function and that an estimate $x_n$ of $x$ is given, consider the monotone…
An analytical approach is developed to the problem of computation of monotone Riemannian metrics (e.g. Bogoliubov-Kubo-Mori, Bures, Chernoff, etc.) on the set of quantum states. The obtained expressions originate from the Morozova, Chencov…
The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function…