Related papers: Critical structures of inner functions
The pressure function is a fundamental object in various areas of mathematics. Its regularity is studied to derive insights into phase transitions in certain physical systems or to determine the Hausdorff dimension of self-affine sets. In…
We investigate magnetic fluctuations of a mesoscopic critical region at the interface induced by smooth time-independent spacial changes of a control parameter across its critical value. Near the spatial critical point, the order parameter…
We present an application-oriented approach to Urysohn and Hammerstein integral operators acting between spaces of H"older continuous functions over compact metric spaces. These nonlinear mappings are formulated by means of an abstract…
Motivated by the vacuum selection problem of string/M theory, we study a new geometric invariant of a positive Hermitian line bundle $(L, h)\to M$ over a compact K\"ahler manifold: the expected distribution of critical points of a Gaussian…
Starting from the De Witt supermetric and limiting ourselves to a family of geometries characterized by a finite number of geometric invariants we extract the unique integration measure. Such a measure turns out to be a geometric invariant,…
The following natural question arises from Shalom's innovational work (1999, Publ. IHES): "Can we establish an intrinsic criterion to synthesize relative fixed point properties into the whole fixed point property without assuming Bounded…
We establish certain fine properties for functions of bounded $\mathscr A$-variation known in the classical $BV$ setting. Here, $\mathscr A$ is a $k$th order constant-coefficient homogeneous linear differential operator with a…
In the present article, composition operators induced by Rational Inner Functions on the bidisc $\mathbb{D}^2$ are studied, acting on the weighted Bergman space $A^2_{\beta}(\mathbb{D}^2).$ We prove that under mild conditions that Rational…
The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…
We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values in infinite-dimensional Banach spaces. We mostly…
An inspiration at the origin of wavelet analysis (when Grossmann, Morlet, Meyer and collaborators were interacting and exploring versions of multiscale representations) was provided by the analysis of holomorphic signals, for which the…
We investigate Liouville-type results, existence, uniqueness and symmetry to the solution of nonlinear nonlocal elliptic equations of the form \[ Lu = |x|^{\gamma}\,H(u)\,G(\nabla u), \qquad x\in\R^n, \] where $L$ is a symmetric,…
The behavior of the critical function for the breakdown of the homotopically non-trivial invariant (KAM) curves for the standard map, as the rotation number tends to a rational number, is investigated using a version of Greene's residue…
We study 2-microlocal Besov and Triebel-Lizorkin spaces with variable exponents on special Lipschitz domains. These spaces are as usual defined by restriction of the corresponding spaces on $\R^n$. In this paper we give two intrinsic…
We consider functions with isolated critical points on a closed surface. We prove that in a neighborhood of a critical point the function conjugates with Re$z^k$ for the some nonnegative integer k. The full topological invariant of such…
In this paper we characterize the zero sets of functions from $\ell^{p}_{A}$ (the analytic functions on the open unit disk $D$ whose Taylor coefficients form an $\ell^p$ sequence) by developing a concept of an "inner function" modeled by…
Let \[ \Gamma = \{(z+w, zw): |z|\leq 1, |w|\leq 1\} \subset \mathbb{C}^2. \] A $\Gamma$-inner function is defined to be a holomorphic map $h$ from the unit disc $\mathbb{D}$ to $\Gamma$ whose boundary values at almost all points of the unit…
We characterize functions of a Bergman space on a square by their values and derivatives on the diagonals. This problem is connected with the reachable space of the one-dimensional heat equation on a finite interval with boundary…
Models of self-organized criticality, which can be described as singular diffusions with or without (multiplicative) Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld- and Zhang-models), are analyzed. Existence and uniqueness of…
We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.