Analysis and Mathematical Physics最新文献

Two interesting phenomena for the construction of quantum states are that of mutually unbiased bases and that of balanced states. We explore a constructive approach to each phenomenon that involves orthogonal polynomials on the unit circle. In the case of mutually unbiased bases, we show that this approach does not produce such bases. In the case of balanced states, we provide examples of pairs of orthonormal bases and states that are balanced with respect to them. We also consider extensions of these ideas to the infinite dimensional setting.

In this article, we investigate sharp functional inequalities associated with the coherent state transforms of the Lie group ( SU(N,1) ). Assuming the isoperimetric conjecture on the complex hyperbolic ball, we establish the Lieb–Wehrl entropy conjecture for ( SU(N,1) ) with ( N ge 2 ). Furthermore, we derive an extension of the Faber–Krahn type inequality within the framework of the Bergman space ( mathcal {A}_{alpha } ).

The paper studies the existence of solutions for the reaction-diffusion equation in (mathbb {R}^2) with point-interaction laplacian (Delta _alpha ) with (alpha in (-infty ,+infty ]), assuming the functions to remain on the absolute continuous projection space. By semigroup estimates, we get the existence and uniqueness of solutions on

with (r>2), (s<frac{2}{r}) for the Cauchy problem with small (T>0) or small initial conditions on (H^1_alpha (mathbb {R}^2)). Finally, we prove decay in time of the functions.

This paper, motivated by the previous one [12], presents some new achievements in estimating Hankel determinants for the class (mathcal {S}) of univalent functions. With the help of the Grunsky inequalities, we improve earlier results for the bound of (H_3(1)) in (mathcal {S}). It is shown that this bound is less than 1. Moreover, we obtain the bounds of (H_3(1)) for univalent functions with the second or the third coefficient vanishing. In particular, the estimate of (H_3(1)) for odd univalent functions is derived.

In this paper we present a ground state solution result for the nonlocal operator such as the generalized p-Laplacian operator with a logarithmic nonlinearity, for which we will use variational methods explicitly the Nehari method.

This article is motivated by the concept of mixed Bohr radius for scalar-valued functions defined in Banach sequence spaces. More precisely, it aims to determine bounds of mixed Bohr radii for holomorphic functions defined on Banach sequence spaces with values in Banach spaces. We determine an upper bound of the mixed Bohr radius by establishing a connection between the mixed Bohr radius and the arithmetic Bohr radius. However, the lower bound is obtained through the implementation of techniques developed recently by Defant, Galicer, Maestre, Mansilla, Muro, and Schwarting.

In this paper, we establish the theory of tetragonal curves and present a systematic method for constructing Riemann theta function solutions to algebro-geometric initial value problems for matrix mKdV equations. Starting from a (4times 4) matrix spectral problem, we derive Lax pairs of matrix mKdV equations using the zero-curvature equation and Lenard equations. The corresponding tetragonal curve is introduced via the characteristic polynomial of the Lax matrices of the hierarchy. Then we discuss Riemann theta functions, the construction of the basis of holomorphic differentials, as well as Abelian differentials of the second and third kinds. Based on the theory of tetragonal curves, we analyze algebro-geometric properties of Baker-Akhiezer functions and a class of meromorphic functions. Finally, we obtain Riemann theta function solutions for the whole matrix mKdV hierarchy through asymptotic analysis.

Let (mathcal {H}) be a separable complex Hilbert space. A conjugate-linear map (C:mathcal {H}rightarrow mathcal {H}) is called a conjugation if it is an involutive isometry. In this paper, we focus on the following interpolation problems: Let ({x_i}_{iin I}) and ({y_i}_{iin I}) be orthonormal sets of vectors in (mathcal {H}), and let ({N_k}_{kin K}) be a set of mutually commuting normal operators. We seek to determine under which conditions there exists a conjugation C on (mathcal {H}) such that

1. (a)

   (Cx_i=y_i) and (CN_kC=N_k^*) for all (iin I) and (kin K); or

2. (b)

   (Cx_i=y_i) and (CN_kC=-N_k^*) for all (iin I) and (kin K).

We provide complete answers to problems (a) and (b) using the spectral projections of normal operators. Our results are then applied to the study of complex-symmetric and skew-symmetric operators, as well as to the characterization of hyperinvariant subspaces of normal operators through conjugations.

In this note, we prove a central limit theorem for the mass distribution of random holomorphic sections associated with a sequence of positive line bundles endowed with (mathscr {C}^{3}) Hermitian metrics over a compact Kähler manifold. In addition, we show that almost every sequence of such random holomorphic sections exhibits quantum ergodicity in the sense of Zelditch.

In this article, we establish weighted estimates for a general class of lacunary maximal functions on homogeneous groups. As an application, we derive weighted estimates for the lacunary maximal function associated to the Korányi spherical means as well as for the lacunary maximal function associated to codimension two spheres in the Heisenberg group, which improves upon previously known results.