Analysis and Mathematical Physics最新文献

In Vinet and Zhedanov (J Phys A Math Theor 45:265304, 2012), while looking for spin chains that admit perfect state transfer, Vinet and Zhedanov found an apparently new sequence of orthogonal polynomials, that they called para-Krawtchouk polynomials, defined on a bilinear lattice. In this note we present necessary and sufficient conditions for the regularity of solutions of the corresponding functional equation. Moreover, the functional Rodrigues formula and a closed formula for the recurrence coefficients are presented. As a consequence, we characterize all solutions of the functional equation, including as very particular cases the Meixner, Charlier, Krawtchouk, Hahn, and para-Krawtchouk polynomials.

In this paper we discuss the boundedness of the Hardy–Littlewood maximal operator (M_{lambda }, lambda ge 1), and the variable Riesz potential operator (I_{alpha (cdot ),tau }, tau ge 1), on Musielak–Orlicz–Morrey spaces (L^{Phi ,kappa ,theta }(X)) over unbounded metric measure spaces X. As an important example, we obtain the boundedness of (M_{lambda }) and (I_{alpha (cdot ),tau }) in the framework of double phase functionals with variable exponents (Phi (x,t) = t^{p(x)} + a(x) t^{q(x)}, x in X, t ge 0), where (p(x)<q(x)) for (xin X), (a(cdot )) is a non-negative, bounded and Hölder continuous function of order (theta in (0,1]). Our results are new even for the variable exponent Morrey spaces or for the doubling metric measure case in that the underlying spaces need not be bounded.

In this article, we study the problem of recovering symmetric m-tensor fields (including vector fields) supported in a unit disk ({mathbb {D}}) from a set of generalized V-line transforms, namely longitudinal, transverse, and mixed V-line transforms, and their integral moments. We work in a circular geometric setup, where the V-lines have vertices on a circle, and the axis of symmetry is orthogonal to the circle. We present two approaches to recover a symmetric m-tensor field from the combination of longitudinal, transverse, and mixed V-line transforms. With the help of these inversion results, we are able to give an explicit kernel description for these transforms. We also derive inversion algorithms to reconstruct a symmetric m-tensor field from its first (m+1) integral moment longitudinal/transverse V-line transforms.

In our previous paper (Golberg et al. in Comput Methods Funct Theory 20(3–4):539–558, 2020), we proved that the complementary components of a ring domain in (mathbb {R}^n) with large enough modulus may be separated by an annular ring domain and applied this result to boundary correspondence problems under quasiconformal mappings. In the present paper, we continue this work and investigate boundary extension problems for a larger class of mappings.

In this paper, we describe holomorphic quantizations of the cotangent bundle of a symmetric space of compact type (T^*(U/K)cong U_mathbb {C}/K_mathbb {C}), along Mabuchi rays of U-invariant Kähler structures. At infinite geodesic time, the Kähler polarizations converge to a mixed polarization (mathcal {P}_infty ). We show how a generalized coherent state transform (gCST) relates the quantizations along the Mabuchi geodesics such that holomorphic sections converge, as geodesic time goes to infinity, to distributional (mathcal {P}_infty )-polarized sections. Unlike in the case of (T^*(U)), the gCST mapping from the Hilbert space of vertically polarized sections are not asymptotically unitary due to the appearance of representation dependent factors associated to the isotypical decomposition for the U-action . In agreement with the general program outlined by Baier, Hilgert, Kaya, Mourão and Nunes in Journal of Geometry and Physics, 2025, we also describe how the quantization in the limit polarization (mathcal {P}_infty ) is given by the direct sum of the quantizations for all the symplectic reductions relative to the invariant torus action associated to the Hamiltonian action of U.

In this paper, two results regarding the existence and multiplicity of ground state solutions for a fractional Kirchhoff-type system involving logarithmic nonlinearities are obtained via variational methods. The proposed problem is motivated by several mathematical models that arise, for example, in quantum mechanics, nuclear physics, quantum optics, transport and diffusion phenomena, effective quantum gravity, open quantum systems, the theory of superfluidity, and Bose–Einstein condensation. The first result provides the existence of a ground state solution for the proposed problem. Under a different set of hypotheses with respect to the first result, a second one is obtained, which provides the existence of at least two non-trivial ground state solutions.

Universal bounds for the potential energy of weighted spherical codes are obtained by linear programming. The universality is in the sense of Cohn-Kumar – every attaining code is optimal with respect to a large class of potential functions (absolutely monotone), in the sense of Levenshtein – there is a bound for every weighted code, and in the sense of parameters (nodes and weights) – they are independent of the potential function. We derive a necessary condition for optimality (in the linear programming framework) of our lower bounds which is also shown to be sufficient when the potential is strictly absolutely monotone. Bounds are also obtained for the weighted energy of weighted spherical designs. We demonstrate our bounds for several previously studied weighted spherical codes.

We establish the comparison principle, existence and regularity of solutions to the following problem concerning the mixed operator:

where (mathcal {M}_{lambda ,Lambda }^+) is the Pucci’s extremal operator and ((-Delta _{mathbbm {H}^N})^s) denotes the fractional sub-Laplacian on the Heisenberg group (mathbbm {H}^N.)

We study metrics on product manifolds which are critical for some quadratic curvature functionals. As a consequence, we provide construction methods and new examples in arbitrary dimension.

We prove a parametric jet interpolation theorem for symplectic holomorphic automorphisms of (mathbb {C}^{2n}) with parameters in a Stein space. Moreover, we provide an example of an unavoidable set for symplectic holomorphic maps.