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81.
Alexander Berkovich S. Ole Warnaar 《Transactions of the American Mathematical Society》2005,357(6):2291-2351
Several new transformations for -binomial coefficients are found, which have the special feature that the kernel is a polynomial with nonnegative coefficients. By studying the group-like properties of these positivity preserving transformations, as well as their connection with the Bailey lemma, many new summation and transformation formulas for basic hypergeometric series are found. The new -binomial transformations are also applied to obtain multisum Rogers-Ramanujan identities, to find new representations for the Rogers-Szegö polynomials, and to make some progress on Bressoud's generalized Borwein conjecture. For the original Borwein conjecture we formulate a refinement based on new triple sum representations of the Borwein polynomials.
82.
83.
84.
LetRIII(n) be the classical domain of typeIII with n≥2. This article is devoted to a deep study of the Schwarz lemma onRIII(n) via not only exploring the smooth boundary points ofRIII(n) but also proving the Schwarz lemma at the smooth boundary point for holomorphic self-mappings ofRIII(n). 相似文献
85.
《Mathematische Nachrichten》2018,291(14-15):2229-2235
We state and prove a refinement of a classical theorem due to Landau on the Koebe domains for certain families of holomorphic functions introduced by A. W. Goodman. Our geometric approach in this article enables us to derive several statements of interest, which would not be produced via the methods in Goodman's paper, as immediate corollaries of the proof of the main theorem. 相似文献
86.
《Mathematische Nachrichten》2018,291(11-12):1757-1768
We consider the class of all sense‐preserving harmonic mappings of the unit disk , where h and g are analytic with , and determine the Bohr radius if any one of the following conditions holds:
- 1. h is bounded in .
- 2. h satisfies the condition in with .
- 3. both h and g are bounded in .
- 4. h is bounded and .
87.
The authors prove a Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces. Roughly speaking, this result says that under a harmonic mapping between the unit balls in real Euclidean spaces, the image of a smaller ball centered at origin can be controlled. This extends the related result proved by Chen in complex plane. 相似文献
88.
In this article, the sharp growth theorem for almost starlike mappings of complex order λ is given firstly. Secondly, distortion theorem along a unit direction is also established as the application of the growth theorem. In particular, using our results can reduce to some well-known results. 相似文献
89.
In this paper, we obtain the strong comparison principle and Hopf Lemma for locally Lipschitz viscosity solutions to a class of nonlinear degenerate elliptic operators of the form ▽~2ψ + L(x, ▽ψ), including the conformal hessian operator. 相似文献
90.
Pavel Yaskov 《Stochastic Processes and their Applications》2018,128(11):3940-3965
We give several extensions of the sewing lemma of Feyel and de La Pradelle and show how these results generalize Young’s integration theory in a simple and natural way. For illustrative purposes, we apply the lemma to integrals involving discontinuous functions of a fractional Brownian motion with the Hurst index 相似文献