典型域上高阶Fréechet导数的Schwarz-Pick估计

本文给出了典型域上带正实部的全纯函数高阶Fr¶echet 导数的Schwarz-Pick 估计. 推广了单位圆盘和单位球上带正实部的全纯函数高阶偏导数的Schwarz-Pick 估计.     

SCHWARZ-PICK ESTIMATES FOR BOUNDED HOLOMORPHIC FUNCTIONS ON CLASSICAL DOMAINS

In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball.     

Higher-Order Schwarz-Pick Estimates for Holomorphic Self-mappings on Classical Domains

In this paper,Schwarz-Pick estimates for high order Fréchet derivatives of holomorphic self-mappings on classical domains are presented.Moreover,the obtained result can deduce the early work on Schwarz...     

单位球上全纯函数的高阶Schwarz-Pick估计*

作者给出了单位球B_n ? Cⁿ到凸区域?? C上全纯函数的高阶Schwarz-Pick估计. 通过引入双曲度量,得到了单位圆盘D到凸区域?上全纯函数的系数估计. 应用该系数估计结果,得到单位球B_n到?内的全纯函数的高阶Schwarz-Pick估计.特别地, 当?是单位圆盘或右半平面时, 得到的结果分别与熟知的结果是一致的.     

关于典型域到单位球上全纯映射的注记

给出了从典型域到单位球的全纯映射高阶Frchet导数的Schwarz-Pick估计,从而推广了单位球上全纯自映射Frchet导数的Schwarz-Pick估计以及单位圆盘上有界全纯函数高阶导数的Schwarz-Pick估计的结论.     

Schwarz-Pick estimates for holomorphic mappings from the polydisk to the unit ball

In this paper, Schwarz-Pick estimates of arbitrary order partial derivatives for holomorphic mappings from the polydisk to the unit ball are presented. We generalize the early work on Schwarz-Pick estimates of higher order derivatives for bounded holomorphic functions on the unit disk and the polydisk.     

A Note on Schwarz-Pick Estimate

A Schwarz-Pick estimate of higher order derivative for holomorphic functions with positive real part on Bn is presented. This improves the earlier work on Schwarz-Pick estimate of higher order derivatives for holomorphic functions with positive real part on the unit disk in C.     

Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc

We give higher order derivatives Schwarz-Pick estimates for all positive real part holomorphic functions on Bn and D n,and generalize early work on Schwarz-Pick estimate of higher order derivatives for holomorphic functions with positive real part on unit disk in C.     

Schwarz-Pick estimates for bounded holomorphic functions in the unit ball of ℂ n

We give a Schwarz-Pick estimate for bounded holomorphic functions on unit ball in Cn, and generalize some early work of Schwarz-Pick estimates for bounded holomorphic functions on unit disk in C.     

Schwarz引理与Schwarz-Pick引理在单位球B_n上的推广

对单复变中的Schwarz引理与Schwarz-Pick引理在C~n中的超球上进行了推广.考虑C~n中单位球B_n上模小于1的全纯函数f(z),并在f(0)=0的条件下给出函数在原点的任意阶导数的估计.更进一步地,得到了B_n上模小于1的任意全纯函数在任意点的高阶导数的估计.     

SCHWARZ-PICK ESTIMATES FOR PARTIAL DERIVATIVES OF ARBITARY ORDER OF BOUNDED HOLOMORPHIC FUNCTIONS IN THE UNIT BALL OF C~n

This paper gives a Schwarz-Pick estimate for bounded holomorphic functions in the unit ball of C n .     

A SCHWARZ-PICK LEMMA FOR THE MODULUS OF HOLOMORPHIC MAPPINGS FROM THE POLYDISK INTO THE UNIT BALL

In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.     

A Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball

In this paper we prove a Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball. This result extends some related results.     

Petersson norms and liftings of Hilbert modular forms

We prove the algebraicity of the ratio of the Petersson norm of a holomorphic Hilbert modular form over a totally real number field and the norm of its Saito-Kurokawa lift. We prove a similar result for the Ikeda lift of an elliptic modular form. In order to obtain these we combine some results on local symplectic groups to generalize a special value of the standard L-function attached to a Siegel-Hilbert cuspform.     

Another look at the Burns-Krantz theorem

We obtain a generalization of the Burns-Krantz rigidity theorem for holomorphic self-mappings of the unit disk in the spirit of the classical Schwarz-Pick Lemma and its continuous version due to L. Harris via the generation theory for one-parameter semigroups. In particular, we establish geometric and analytic criteria for a holomorphic function on the disk with a boundary null point to be a generator of a semigroup of linear fractional transformations in term of relations among three boundary derivatives of the function at this point.     

A Theorem of Beurling-sLax Type for Hilbert Spaces of Functions Analytic in the Unit Ball

Schur multipliers on the unit ball are operator-valued functions for which the N-variable Schwarz-Pick kernel is nonnegative. In this paper, the coefficient spaces are assumed to be Pontryagin spaces having the same negative index. The associated reproducing kernel Hilbert spaces are characterized in terms of generalized difference-quotient transformations. The connection between invariant subspaces and factorization is established.     

Hilbert polynomials and Arveson's curvature invariant

We define and study Hilbert polynomials for certain holomorphic Hilbert spaces. We obtain several estimates for these polynomials and their coefficients. Our estimates inspire us to investigate the connection between the leading coefficients of Hilbert polynomials for invariant subspaces of the symmetric Fock space and Arveson's curvature invariant for coinvariant subspaces. We are able to obtain some formulas relating the curvature invariant with other invariants. In particular, we prove that Arveson's version of the Gauss-Bonnet-Chern formula is true when the invariant subspaces are generated by any polynomials.     

Vitali's and Harnack's type results for vector-valued functions

In this brief note, we extend Vitali's theorem for holomorphic functions obtained by Arendt and Nikolski to nets of functions of sheaves of smooth vector-valued functions. As a consequence we also extend a Harnack's theorem for compact operator-valued harmonic functions recently obtained by Enflo and Smithies to bounded operator-valued harmonic functions, avoiding the assumption that the Hilbert space H where the operators are defined is separable.     

High-order Schwarz-Pick Lemma for the Schur class on the polydisc

In this paper, we give Schwarz-Pick Lemma for functions in the Schur class on the polydisc of ? ⁿ , and generalize some early work of Schwarz-Pick Lemma for functions in the Schur class on the unit disk of C and functions in the Schur-Agler class on the polydisc of ? ⁿ .     

Holomorphic Hermite functions and ellipses

In 1990 van Eijndhoven and Meyers introduced systems of holomorphic Hermite functions and reproducing kernel Hilbert spaces associated with the systems on the complex plane. Moreover they studied the relationship between the family of all their Hilbert spaces and a class of Gelfand–Shilov functions. After that, their systems of holomorphic Hermite functions have been applied to studying quantization on the complex plane, combinatorics, and etc. On the other hand, the author recently introduced systems of holomorphic Hermite functions associated with ellipses on the complex plane. The present paper shows that their systems of holomorphic Hermite functions are determined by some cases of ellipses, and that their reproducing kernel Hilbert spaces are some cases of the Segal–Bargmann spaces determined by the Bargmann-type transforms introduced by Sjöstrand.