泛函分析

We shown that every continuous local functional on the space of finite convex functions on $\mathbb{R}^n$ is a valuation. This relation is used to establish a homogeneous decomposition for the class of polynomial local functionals as well…

We consider evolutionary equations as introduced by R.\ Picard in 2009 and develop a general theory for approximation which can be seen as a theoretical foundation for numerical analysis for evolutionary equations. To demonstrate the…

The main aim of this paper is to obtain Bochkarev-type inequalities for the anisotropic grand Lorentz spaces. In the classical setting, Bochkarev obtained inequalities of the Hardy--Littlewood type, which reveal the connection between the…

We investigate the interplay among three key properties of bounded linear operators between Banach spaces: the Bhatia-\v{S}emrl property, strong subdifferentiability and the condition that the essential norm is strictly less than the…

We consider the problem of whether there is a sequence of homeomorphisms $(F_k)_k$ between the unit spheres of the $k$-dimensional Banach spaces $\ell_\infty^k$ and $\ell_1^k$ which is also equi-uniformly continuous. We prove that this…

This paper develops a fixed point version of the well-known Nehari manifold method from critical point theory. The main result is formulated for systems of operator equations, relying on the fixed point theorems of Schauder and Schaefer.…

Let $0 \leq \alpha < n$, $N \in \mathbb{N}$, and let $X$ and $Y$ be ball quasi-Banach function spaces on $\mathbb{R}^n$. We consider operators $T_{\alpha}$ defined by convolution with kernels of type $(\alpha, N)$. Assuming that the powered…

In their 2022 lecture notes on condensed sets, Clausen and Scholze mentioned in a remark that the important subclass of quasiseparated condensed sets is equivalent to the category of so-called compactological spaces defined by Waelbroeck in…

We extend the classical Fuglede commutativity theorem to the full scale of symmetrically normed operator ideals. Our main result provides a complete characterization: a symmetric ideal or symmetric operator space of $\tau$-measurable…

This paper investigates new properties of $q$-numerical ranges for compact normal operators and establishes refined upper bounds for the $q$-numerical radius of Hilbert space operators. We first prove that for a compact normal operator $T$…

Consider a continuous bundle $\mathcal{E}\to X$ of Banach/Hilbert spaces or Banach/$C^*$-algebras over a paracompact base space, equivariant for a compact Lie group $\mathbb{U}$ operating on all structures involved. We prove that in all…

We show that the smoother the weight, the broader the range of exponents for which the Lavrentiev's gap is absent for the double phase functionals, i.e., $u \mapsto \int_{\Omega} \left(|\nabla u|^p + a(x)|\nabla u|^q\right)\,dx\,, \quad 1…

We revisit the mean field parametrization of shallow neural networks, using signed measures on unbounded parameter spaces and duality pairings that take into account the regularity and growth of activation functions. This setting directly…

This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…

In this paper, we introduce the concept of cyclic orbital contraction mappings which generalizes the concept of cyclic contraction mappings. We establish the existence of best proximity point of these mappings in the framework of $CAT_p(0)$…

Using ideas from algebraic $K$-theory, we prove that a simple and naturally applicable criterion of Kitaev suffices to trivialize the Fredholm determinant of a multiplicative commutator.

Let $\mathcal{H}$ be a complex finite-dimensional or infinite-dimensional separable Hilbert space, $\mathcal{B(H)}$ and $\mathcal{T(H)}$ be the Banach spaces of all bounded linear operators and of all trace class operators on $\mathcal{H},$…

We develop a unified approach to defining a point at infinity for an arbitrary space and formalizing convergence to this point. Central to our work is a method to quantify and classify the rates at which functions approach their limits at…

Let E be a Dedekind complete Riesz space with weak unit e, equipped with a conditional expectation operator T. We prove that the spaces Lp(T), with their natural vector-valued norms, are strongly complete, extending the p=2 case of Kuo,…

In this paper, we elucidate certain properties of the $(2n+1)$-dimensional Heisenberg group, and establish some theorems on the invariant differential operators on the group.