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1.
In this paper the Dirichlet problem for pluriholomorphic functions of two complex variables is investigated. The key point is the relation between pluriholomorphic functions and pluriharmonic functions. The link is constituted by the Fueter-regular functions of one quaternionic variable. Previous results about the boundary values of pluriharmonic functions and new results on L2 traces of regular functions are applied to obtain a characterization of the traces of pluriholomorphic functions.  相似文献   

2.
In the present paper, we introduce and investigate classes of analytic functions involving the Srivastava-Attiya operator. Basic properties for β-uniformly starlike functions of order γ are studied, such as inclusion relations, sufficient conditions, coefficient inequalities and distortion inequalities. The results are also extended to β-uniformly convex, close-to-convex, and quasi-convex functions. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.  相似文献   

3.
Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g=f−1 satisfying the conditions that zf(z)/f(z) and zg(z)/g(z) are both subordinate to a univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are made.  相似文献   

4.
We examine classes of real-valued functions of 0-1 variables closed under algebraic operations as well as topological convergence, and having a certain local characteristic (requiring that any function not in the class should have a k-variable minor not belonging to this class). It is shown that for k=2, the only 4 maximal classes with these properties are those of submodular, supermodular, monotone increasing and monotone decreasing functions. All the 13 locally defined closed classes are determined and shown to be intersections of the 4 maximal ones. All maximal classes for k≥3 are determined and characterized by the sign of higher order derivatives of the functions in the class.  相似文献   

5.
Univariate specializations of Appell's hypergeometric functions F1, F2, F3, F4 satisfy ordinary Fuchsian equations of order at most 4. In special cases, these differential equations are of order 2 and could be simple (pullback) transformations of Euler's differential equation for the Gauss hypergeometric function. The paper classifies these cases, and presents corresponding relations between univariate specializations of Appell's functions and univariate hypergeometric functions. The computational aspect and interesting identities are discussed.  相似文献   

6.
In this note we discuss a few properties of transnormal Finsler functions, i.e., the natural generalization of distance functions and isoparametric Finsler functions. In particular, we prove that critical level sets of an analytic transnormal function are submanifolds, and the partition of M into level sets is a Finsler partition, when the function is defined on a compact analytic manifold M.  相似文献   

7.
In this paper we obtain the sharp lower bound for , for functions f that are k-uniformly convex in the unit disk U. Next we consider the problem of finding the minimum of for functions f that are k-uniformly convex in the disk of radius r. Corresponding results for the class of starlike functions related to the class of k-uniformly convex functions are presented.  相似文献   

8.
Progressive functions at time t involve only the progressive functions at time before t and some nice compactly supported function at time t. We give sufficient conditions and explicit formulas to construct progressive functions with exponential decay and characterize the conditions on which the positive integer translates of a progressive function are orthonormal or a Riesz sequence. We provide explicit ways for construction of orthonormal progressive functions and for construction of the biorthogonal functions of nonorthogonal progressive functions. Such progressive functions can be used to construct wavelets with arbitrary smoothness on the half line if they are generated by a smooth refinable compactly supported function.  相似文献   

9.
The aim of this paper is to study and discuss the action of the Hecke operators to not only the generalized the Weber-type functions, but also the kth derivative of the Weierstrass-type functions. Furthermore, relations related to the Weierstrass-type functions and Riemann zeta and theta function are found.  相似文献   

10.
Asymptotic expansions are given for large values of n of the generalized Bessel polynomials . The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the origin in the z-plane. New forms of expansions in terms of elementary functions valid in sectors not containing the turning points zi/n are derived, and a new expansion in terms of modified Bessel functions is given. Earlier asymptotic expansions of the generalized Bessel polynomials by Wong and Zhang (1997) and Dunster (2001) are discussed.  相似文献   

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