The Gleason''''s problem for some polyharmonic and hyperbolic harmonic function spaces

LetΩ Rn be a bounded convex domain with C2 boundary. For 0相似文献   

The Gleason''''s problem on mixed norm spaces in convex domains

Let Ω be a bounded convex domain with C2 boundary in C2 and for given 0 < p, q ≤∞ and normal weight function (r) let Hp,q, be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω, a, Hp,q,) is solvable for any fixed point a ∈ Ω. While solving the Gleason's problem we obtain the boundedness of certain integral operator on Hp,q,.     

C ∞-isometric imbeddings of the hyperbolic plane and of cylinders with hyperbolic metric in spherical spaces

Summary C^∞ — isometric imbeddings of the hyperbolic plane and of the two types of orientable cylinders with hyperbolic metric in spherical8-space are constructed, furthermore C^∞ — isometric imbeddings of the non-orientable cylinder with hyperbolic metric in Euclidean8-space and in spherical10-space. To Enrico Bompiani on his scientific Jubilee.     

On orthogonality-preserving plücker transformations of hyperbolic spaces

A complete overview of all orthogonality-preserving Plücker transformations in finite dimensional hyperbolic spaces with dimension other than three is given. In the Cayley-Klein model of such a hyperbolic space all Plücker transformations are induced by collineations of the ambient projective space.     

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Analytic solution of an ℝ-linear conjugation problem in the case of hyperbolic interface

We derive an explicit analytical solution for the conjugation problem in a heterogeneous infinite planar structure consisting of two dissimilar homogeneous media with two branches of a hyperbola as an interface. We investigate both cases involving real and complex coefficients of the corresponding boundary condition.     

On the uniqueness problem of differential equations in normed spaces †

Simple direct proofs of some recent results by Kalla, Conde, and Hubbell for a generalized elliptic type integral [Appl. Anal., 22 (1986), pp. 273-287] are presented. Furthermore, a new single term asymptotic approximation for this function is derived, which is superior to the two term approximation given by these authors     

Density of the polynomials in Hardy and Bergman spaces of slit domains

It is shown that for any t, 0<t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that G\{1} í \mathbbD:={z:|z| < 1}\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\} and with the property that the analytic polynomials are dense in the Bergman space \mathbbA^t(\mathbbD\G)\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma) . It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous real-valued function on [0,1], where the polynomials are dense in H^t(\mathbbD\G)H^{t}(\mathbb{D}\setminus\Gamma) ; improving upon a result in an earlier paper.     

The Gleason’s problem for some polyharmonic and hyperbolic harmonic function spaces

Let Ω ⊆ ℝⁿ be a bounded convex domain with C ² boundary. For 0 < p, q ⩽ ∞ and a normal weight φ, the mixed norm space H _k ^p,q,φ (Ω) consists of all polyharmonic functions f of order k for which the mixed norm ∥ · ∥_p,q,φ < ∞. In this paper, we prove that the Gleason’s problem (Ω, a, H _k ^p,q,φ ) is always solvable for any reference point a ∈ Ω. Also, the Gleason’s problem for the polyharmonic φ-Bloch (little φ-Bloch) space is solvable. The parallel results for the hyperbolic harmonic mixed norm space are obtained.     

Flensted-Jensen’s functions attached to the Landau problem on the hyperbolic disc

We give an explicit expression of a two-parameter family of Flensted-Jensen’s functions Ψ _μα on a concrete realization of the universal covering group of U(1, 1). We prove that these functions are, up to a phase factor, radial eigenfunctions of the Landau Hamiltonian on the hyperbolic disc with a magnetic field strength proportional to μ, and corresponding to the eigenvalue 4α(α − 1).     

Double integral characterizations of harmonic Bergman spaces

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Moment vanishing properties of harmonic Bergman functions

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Forelli-Rudin type theorem in pluriharmonic Bergman spaces with small index

It is proved that the Bergman type operatorT, is a bounded projection from the pluriharmonic Bergman spaceL ^p (B)∩h(B) onto Bergman spaceL ^p (B) ∩ H(B) for 0p 1 ands (p¹-1)(n+1). As an application it is shown that the Gleason’s problem can be solved in Bergman space L^P(B)∩H(B) for 0p 1. Project supported by the National Natural Science Foundation of China (Grant No. 19871081) and the Doctoral Program Foundation of the State Education Commission of China.     

On a multiplicity one property for the length spectra of even dimensional compact hyperbolic spaces

We prove a multiplicity one theorem for the length spectrum of compact even dimensional hyperbolic spaces, i.e., if all but finitely many closed geodesics for two compact even dimensional hyperbolic spaces have the same length, then all closed geodesics have the same length.     

Boundary behavior in Hilbert spaces of vector-valued analytic functions

In this paper we study the boundary behavior of functions in Hilbert spaces of vector-valued analytic functions on the unit disc D. More specifically, we give operator-theoretic conditions on Mz, where Mz denotes the operator of multiplication by the identity function on D, that imply that all functions in the space have non-tangential limits a.e., at least on some subset of the boundary. The main part of the article concerns the extension of a theorem by Aleman, Richter and Sundberg in [A. Aleman, S. Richter, C. Sundberg, Analytic contractions and non-tangential limits, Trans. Amer. Math. Soc. 359 (2007)] to the case of vector-valued functions.     

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