Related papers: Functions of Several Variables
In this paper we determine the region of variability for spirallike funcions with respect to a boundary point. In the final section we graphically illustrate the region of variability for several sets of parameters.
We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…
An introduction to geometric valuation theory is given. The focus is on classification results for $\operatorname{SL}(n)$ invariant and rigid motion invariant valuations on convex bodies and on convex functions.
Global deformations of surfaces, immersed into the Euclidean 3-space, by using the modified Novikov--Veselov equation are investigated. relation to the theory of the Willmore functional is discussed
We obtain a description of the homeomorphisms which induce bounded composition operators on Sobolev spaces of functions on metric measure spaces.
The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalites for functions. This will allow us to prove a local subelliptic Sobolev inequality with the optimal…
We review results of {\v{S}}ver\'{a}k, and Goldstein-Haj{\l}asz-Pakzad on how to show the continuity of functions in a critical Sobolev space with positive Jacobian. In the final chapter we expand on the theory of $VMO$ functions, showing a…
These are notes from a basic course in Several Complex Variables
We introduce and analyse a class of weighted Sobolev spaces with mixed weights on angular domains. The weights are based on both the distance to the boundary and the distance to the one vertex of the domain. Moreover, we show how the…
CONTENTS: 1 Introduction 2 Analytic Manifolds and Analytic Continuation of Metrics 3 Walker's Spacetimes and their Maximal Extension 4 Global Structure of de Sitter and Reissner-Nordstr\"om-de Sitter Cosmos 4.1 Special Cases 4.2 Collapsing…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
Graph-based analysis holds both theoretical and applied significance, attracting considerable attention from researchers and yielding abundant results in recent years. However, research on fractional problems remains limited, with most of…
A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…
The aim of this paper is to provide Markov-type inequalities in the setting of weighted Sobolev spaces when the considered weights are generalized classical weights. Also, as results of independent interest, some basic facts about Sobolev…
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…
Reeb spaces of smooth functions are fundamental and strong tools in understanding manifolds via smooth functions with mild critical points. They are defined as the natural spaces of all connected components of level sets. They are also…
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 Laplace operator on domains subject to Dirichlet or Neumann boundary conditions. We show that these operators admit a bounded $H^{\infty}$-functional calculus on weighted Sobolev spaces, where the weights are powers of the…
The reappearance of a sometimes called exotic behavior for linear and multilinear pseudodifferential operators is investigated. The phenomenon is shown to be present in a recently introduced class of bilinear pseudodifferential operators…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…