Analysis and Mathematical Physics最新文献

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.

We study the existence of normalized solutions to the following p-Laplacian Choquard equation

having prescribed mass

where (c>0), (lambda in mathbb {R}) is the Lagrange multiplier, (*) indicates the convolution operator and (Delta _p u=textrm{div}left( |nabla u|^{p-2}nabla uright) ) denotes the usual p-Laplacian operator with (2le p<N). Under different assumptions on c and q, on the one hand, we proved the existence of the normalized ground state solution if (p_{alpha }=frac{(N+alpha )p}{2N}<q<bar{p}=frac{p(p+N+alpha )}{2N}), on the other hand, we obtained the existence of one local minimum type solution and one mountain pass solution with the prescribed mass (cin (0,c_0)) if (bar{p}<q<p_{alpha }^*=frac{(N+alpha )p}{2(N-p)}). In addition, the detailed elaboration is provided for the best constant of interpolation inequality as well as the by-product of the proof process such as a compact embedding result.

Let U be a bounded domain in (mathbb C^d) and let (L^p_a(U)), (1 le p < infty ), denote the space of functions that are analytic on (overline{U}) and bounded in the (L^p) norm on U. A point (x in overline{U}) is said to be a bounded point evaluation for (L^p_a(U)) if the linear functional (f rightarrow f(x)) is bounded in (L^p_a(U)). In this paper, we provide a purely geometric condition given in terms of the Sobolev q-capacity for a point to be a bounded point evaluation for (L^p_a(U)). This extends results known only for the single variable case to several complex variables.

In this work, the explicit expressions of coefficients involved in quasi Christoffel polynomials of order one and quasi-Geronimus polynomials of order one are determined for Jacobi polynomials. These coefficients are responsible for establishing the orthogonality of quasi-spectral polynomials of Jacobi polynomials. Additionally, the orthogonality of quasi-Christoffel Laguerre polynomials of order one is derived. In the process of achieving orthogonality, in both cases, one zero is located on the boundary of the support of the measure. This allows us to derive the chain sequence and minimal parameter sequence at the point lying at the end point of the support of the measure. Furthermore, the interlacing properties among the zeros of quasi-spectral orthogonal Jacobi polynomials and Jacobi polynomials are illustrated. Finally, we define the quasi-Christoffel polynomials of order one on the unit circle and analyze the location of their zeros for specific examples, as well as propose the problem in the general setup.

In this paper, we give a short summary of fractal calculus. We introduce the concept of fractal variation of calculus and derive the general form of the fractal Euler equation, along with an alternate form. We explore applications of the fractal Euler equation, including the optical fractal path near the event horizon of a black hole and determining the shortest distance in fractal space. Examples and illustrative plots are provided to demonstrate the detailed behavior of these equations and their practical implications.

Let (s,bin mathbb {R}). This article is devoted to establishing the Fourier-analytical characterization of the pointwise multiplier space (M(B^{s,b}_{p,q}(mathbb {R}^n))) for the logarithmic Besov space (B^{s,b}_{p,q}(mathbb {R}^n)) in the endpoint cases, that is, (p,qin {1,infty }). The authors first obtain such a characterization for the cases where (p=1) and (q=infty ) and where (p=infty ) and (q=1). Applying this, the authors then establish the duality formula (M(B^{s,b}_{p,q}(mathbb {R}^n))=M(B^{-s,-b}_{p',q'}(mathbb {R}^n)),) where (s,bin mathbb {R}), (p,qin [1,infty ]), and (p') and (q') are respectively the conjugate indices of p and q. This duality principle is further applied to establish the Fourier-analytical characterization of (M(B^{s,b}_{p,q}(mathbb {R}^n))) in the cases where (p=infty =q) and where (p=1=q).

This work derives novel exact solutions of the Biswas–Milovic nonlinear Schrödinger equation by employing the innovative Extended Modified Auxiliary Equation Mapping Technique, augmented with enhanced sensitivity analysis. The resulting bright, kink, anti-kink, and periodic soliton solutions provide deep insights into the complex dynamics of nonlinear wave propagation. To unravel the intricate behaviors of these solitons, we analyze phase trajectories, density distributions, and streamlines, with a particular focus on their sensitivity to initial conditions. Stability is rigorously evaluated through a Hamiltonian formalism, ensuring both analytical rigor and structural robustness. Collectively, these findings enrich the theoretical understanding of soliton dynamics and open new pathways for practical applications in advanced physical systems.