Analysis and Mathematical Physics最新文献

For the Reshetnyak-class homeomorphisms (varphi :Omega rightarrow Y), where (Omega ) is a domain in some Carnot group and Y is a metric space, we obtain an equivalent description as the homeomorphisms which induce the bounded composition operator

where (1le qle infty ), as (varphi ^*u=ucirc varphi ) for (uin textrm{Lip}(Y)). We demonstrate the utility of our approach by characterizing the homeomorphisms (varphi :Omega rightarrow Omega ') of domains in some Carnot group ({mathbb {G}}) which induce the bounded composition operator

on homogeneous Sobolev spaces. The new proof of this known criterion is much shorter than the one already available, requires a minimum of tools, and enables us to obtain new properties of the homeomorphisms in question.

It is known that the Funk transform (FT) is invertible in the class of even (symmetric) continuous functions defined on the unit 2-sphere ({textbf{S}}^{2}). In this article, for the reconstruction of (fin { {mathcal {C}}}^{1}({textbf{S}}^{2})) (can be non-even), an additional condition is found, which is a weighted Funk transform (to reconstruct an odd function), and the injectivity of the so-called two data Funk transform is considered. The transform consists of the classical FT and the weighted FT. An iterative inversion formula of the transform is presented. Such inversions have theoretical significance in convexity theory, integral geometry and spherical tomography.

In this article we investigate the property of complete monotonicity within a special family (mathcal {F}_s) of functions in s variables involving logarithms. The main result of this work provides a linear isomorphism between (mathcal {F}_s) and the space of real multivariate polynomials. This isomorphism identifies the cone of completely monotone functions with the cone of non-negative polynomials. We conclude that the cone of completely monotone functions in (mathcal {F}_s) is semi-algebraic. This gives a finite time algorithm to decide whether a function in (mathcal {F}_s) is completely monotone.

Let (-Delta _{mathcal {S}}) be the Laplace operator in (mathcal{S} subset mathbb {R}^3) on a waveguide shaped surfaces, i.e., ({mathcal {S}}) is built by translating a closed curve in a constant direction along an unbounded spatial curve. Under the condition that the tangent vector of the reference curve admits a finite limit at infinity, we find the essential spectrum of (-Delta _{mathcal {S}}) and discuss conditions under which discrete eigenvalues emerge. Furthermore, we analyze the Laplacian in the case of a broken sheared waveguide shaped surface.

This paper studies the degenerate kernel approximation theory for the second-kind Fredholm integral equations in (L^p) spaces ((1 leqslant p leqslant infty )). By introducing the mixed norm of kernel functions to construct an adaptive analytical tool, the research framework is extended from the classical (L^2) space to the more general (L^p) spaces. Based on the degenerate kernel approximation method, through refined norm estimation of iterated kernels and convergence analysis of the resolvent kernel series, the resolvent kernel representation theory for the solution of integral equations is established. This weakens the strong constraints on the growth of kernel functions and improves the applicability of the theory to non-compact intervals and weakly decaying kernel scenarios. On this basis, two types of error estimations are proposed: dual resolvent kernel error estimate and single resolvent kernel error estimate, which clearly characterize the error relationship between the approximate solution and the exact solution. This research provides a unified framework for the analysis of solutions to integral equations with different regularity characteristics and improves the system of integral equation approximation theory. Furthermore, the degenerate kernel approximation theory and error estimation results established in this paper can be directly extended to integral equations in high-dimensional Euclidean spaces, and their analytical framework and conclusions remain valid in high-dimensional cases.

Let (varphi :{mathbb {D}} rightarrow {mathbb {D}}) be a parabolic self-map of the unit disc ({mathbb {D}}) having zero hyperbolic step. We study holomorphic self-maps of ({mathbb {D}}) commuting with (varphi ). In particular, we answer a question from Gentili and Vlacci (1994) by proving that (psi in mathsf {Hol({mathbb {D}},{mathbb {D}})}) commutes with (varphi ) if and only if the two self-maps have the same Denjoy – Wolff point and (psi ) is a pseudo-iterate of (varphi ) in the sense of Cowen. Moreover, we show that the centralizer of (varphi ), i.e. the semigroup ({mathscr {Z}}_forall (varphi ):={psi in mathsf {Hol({mathbb {D}},{mathbb {D}})}:psi circ varphi =varphi circ psi }) is commutative. We also prove that if (varphi ) is univalent, then all elements of ({mathscr {Z}}_forall (varphi )) are univalent as well, and if (varphi ) is not univalent, then the identity map is an isolated point of ({mathscr {Z}}_forall (varphi )). The main tool is the machinery of simultaneous linearization, which we develop using holomorphic models for iteration of non-elliptic self-maps originating in works of Cowen and Pommerenke.

Choi-Wang obtained a lower bound of the first eigenvalue of the Laplacian on closed minimal hypersurfaces. On minimal hypersurfaces with boundary, Fraser-Li established an inequality giving a lower bound of the first Steklov eigenvalue as a counterpart of the Choi-Wang inequality. The Fraser-Li type inequality was obtained for manifolds with non-negative Ricci curvature. In this paper, we extend it to the setting of non-negative Ricci curvature with respect to the Wylie-Yeroshkin type affine connection. Our results apply to both weighted Riemannian manifolds with non-negative 1-weighted Ricci curvature and substatic triples.

The aim of this paper is to investigate a higher upper and lower decay rates for the difference (u-{tilde{u}}) where (u) is a strong or classical solution of an incompressible (non-)Newtonian fluid in ({{mathbb {R}} }^3) with the initial data (u_0) and ({tilde{u}}) is the strong or classical solution of the same equations with large perturbed initial data (W_0). The proof is based on energy estimates.

We study the interplay between spectrum, geometry and boundary conditions for two distinguished self-adjoint realisations of the Laplacian on infinite metric graphs, the so-called Friedrichs and Neumann extensions. We introduce a new criterion for compactness of the resolvent and apply this to identify a transition from purely discrete to non-empty essential spectrum among a class of infinite metric graphs, a phenomenon that seems to have no known counterpart for Laplacians on Euclidean domains of infinite volume. In the case of discrete spectrum we then prove upper and lower bounds on eigenvalues, thus extending a number of bounds previously only known in the compact setting to infinite graphs. Some of our bounds, for instance in terms of the inradius, are new even on compact graphs.