泛函分析

The aim of this paper is to establish a strong convergence theorem for a strongly nonexpansive sequence in a Banach space. We also deal with some applications of the convergence theorem.

We introduce an analogue of Riesz $s$-potetial and $s$-energy, $0<s<1$, of a mass distribution $\mu$ on the Cantor dyadic group $G$ by defining a respactive $s$-kernel. Then we relate Hausdorff dimension of a set $E\subset G$ to the value…

In this paper we provide spectral inclusion and mapping theorems for strongly continuous locally equicontinuous semigroups on Hausdorff locally convex spaces. Our results extend the classical spectral inclusion and mapping theorems for…

We develop a rigorous measure-theoretic framework for the analysis of fixed points of nonexpansive maps in the space $L^1(\mu)$, with explicit consideration of quantization errors arising in fixed-point arithmetic. Our central result shows…

In 1989, A. J. Duran [Proc. Amer. Math. Soc. 107 (1989), 731-741] showed, that for every complex sequence $(s_\alpha)_{\alpha\in\mathbb{N}_0^n}$ there exists a Schwartz function $f\in\mathcal{S}(\mathbb{R}^n,\mathbb{C})$ with…

Let $\Phi$ be an $N$-function whose Matuszewska-Orlicz indices satisfy $1<\alpha_\Phi\le\beta_\Phi<\infty$. Using these indices, we introduce ``interpolation friendly" classes of Fourier multipliers $M_{[\Phi]}$ and $M_{\langle\Phi\rangle}$…

Using tools from the theory of optimal transport, we establish several results concerning isometric actions of amenable topological groups with potentially unbounded orbits. Specifically, suppose $d$ is a compatible left-invariant metric on…

We study the 'bad science matrix problem': among all matrices $A\in\mathbb{R}^{n\times n}$ whose rows have unit $\ell_2$-norm, determine the maximum of $\beta(A)=\frac{1}{2^n}\sum_{x\in\{\pm1\}^n}\|Ax\|_\infty$. Steinerberger [1]…

In this article, we generalize the definition of the probabilistic Gel'fand width from the Hilbert space to the strictly convex reflexive space by giving Birkhoff left orthogonal decomposition theorem. Meanwhile, a more natural definition…

Given a real valued function having a nondegenerate compact manifold of critical points, some of these points survive under small $C^2$ perturbations. This is a well-known result in critical point theory. In 1986 Weinstein obtained the…

This paper studies absolute integrability for functions with values in semi- normed spaces and in locally convex topological vector spaces (LCTVS). We introduce an \emph{upper-integral} approach (based on a $\rho$-variational measure…

In this paper we prove boundedness of Calder\'on-Zygmund operators and the Christ-Goldberg maximal operator in the matrix-weighted variable Lebesgue spaces recently introduced by Cruz-Uribe and the second author. Our main tool to prove…

In this paper, we investigate contractive projections, conditional expectations, and idempotent coefficient multipliers on the Hardy spaces $H^p(\mathbb{T})$ for $0<p<1$. For such values of $p$, we first establish a general extension…

Through the establishment of several extension theorems, we provide explicit expressions for all contractive projections and 1-complemented subspaces in the Hardy space $H^p(\mathbb{T})$ for $1\leq p<\infty$, $p\neq 2$. Our characterization…

The goal of this paper is to unify the theory of weights beyond the setting of weighted Lebesgue spaces in the general setting of quasi-Banach function spaces. We prove new characterizations for the boundedness of singular integrals, pose…

We investigate Wiener's Tauberian theorem from the perspective of limit functions, which results in several new versions of the Tauberian theorem. Based on this, we formulate and prove analogous Tauberian theorems for operators in the sense…

Let $r \in \mathbb{N}\cup\{\infty\}$ be a fixed number and let $P_j\,\, (1 \leq j\leq r )$ be the projection onto the closed subspace $\mathcal{M}_j$ of $\mathscr{H}$. We are interested in studying the sequence $P_{i_1}, P_{i_2}, \ldots…

An operator $T$ on a Hilbert space $\mathcal H$ is called expansive, if $\|Tx\|\geq \|x\|$ ($x\in\mathcal H$). Expansive operators $T$ quasisimilar to the unilateral shift $S_N$ of finite multiplicity $N$ are studied. It is proved that…

The notion of isometric and unitary asymptotes was introduced for power bounded operators in 1989 and was generalized in 2016--2019 by K\'erchy. In particular, it was shown that there exist operators without unitary asymptote. In this paper…

This paper presents new approaches to the fixed point property for nonexpansive mappings in L^1 spaces. While it is well-known that L^1 fails the fixed point property in general, we provide a complete and self-contained proof that…