Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...

The classical Trudinger-Moser inequality says that for functions with Dirichlet norm smaller or equal to 1 in the Sobolev space H 0 (Ω) (with Ω ⊂ R a bounded domain), the integral ∫ Ω e 2 dx is uniformly bounded by a constant depending only on Ω. If the volume |Ω| becomes unbounded then this bound tends to infinity, and hence the Trudinger-Moser inequality is not available for such domains (and...

We investigate the problem of estimating the number of modes (i.e., local maxima)—a well known question in statistical inference—and we show how to do so without presmoothing the data. To this end, we modify the ideas of persistence barcodes by first relating persistence values in dimension one to distances (with respect to the supremum norm) to the sets of functions with a given number of mode...

Denote by Ln the projection operator obtained by applying the Lagrange interpolation method, weighted by (1 − x), at the zeros of the Chebyshev polynomial of the second kind of degree n + 1. The norm ‖Ln‖ = max ‖f‖∞≤1 ‖Lnf‖∞, where ‖ · ‖∞ denotes the supremum norm on [−1, 1], is known to be asymptotically the same as the minimum possible norm over all choices of interpolation nodes for unweight...

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

For purposes of actual evaluation, mathematical functions f are commonly replaced by approximation polynomials p. Examples include floating-point implementations of elementary functions, quadrature or more theoretical proof work involving transcendental functions. Replacing f by p induces a relative error ε = p/f −1. In order to ensure the validity of the use of p instead of f , the maximum err...

We prove two-weight norm inequalities for Cesàro means of generalized Hermite polynomial series and for the supremum of these means. A result about weak boundedness and an almost everywhere convergence result are also obtained.

We prove that the transfer operator for a general class of rational maps converges exponentially fast in the supremum norm and in HH older norms for small enough HH older exponents to its principal eigendirection.