共查询到20条相似文献,搜索用时 9 毫秒
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Stephen J. Gardiner 《Transactions of the American Mathematical Society》1996,348(1):251-265
Let be an open set in and be a relatively closed subset of . We characterize those pairs which have the following property: every function which is bounded and continuous on and harmonic on can be uniformly approximated by functions harmonic on . Several related results concerning both harmonic and superharmonic approximation are also established.
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Keiji Izuchi Shû ichi Ohno 《Proceedings of the American Mathematical Society》2006,134(5):1359-1364
We study Hankel-type operators on the space of bounded harmonic functions on the open unit disk. These operators are related to tight uniform algebras, the Dunford-Pettis property, and Bourgain algebras.
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We discuss determination of jumps for functions with generalized bounded variation. The questions are motivated by A. Gelb
and E. Tadmor [1], F. Móricz [5] and [6] and Q. L. Shi and X. L. Shi [7]. Corollary 1 improves the results proved in B. I.
Golubov [2] and G. Kvernadze [3].
Supported by NSFC 10671062. 相似文献
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Alexander J. Izzo 《Proceedings of the American Mathematical Society》2007,135(4):1065-1071
Let denote the open unit disc, and let denote the disc algebra. The subsets of such that the inclusion holds for every nonconstant continuous on , or the inclusion holds for every bounded harmonic nonholomorphic function on continuous on , are characterized. In the first case the condition is that has positive measure, and in the second case that has full measure in .
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A. N. Bakhvalov 《Moscow University Mathematics Bulletin》2007,62(1):12-17
An example of a function of four variables belonging to the class of bounded harmonic variation (in a weak sense) is constructed. Cubic sums of a trigonometric Fourier series for this function does not possess the localization property. 相似文献
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A. R. Nurbekyan A. A. Sahakyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2014,49(4):157-165
The paper considers a question of convergence of partial sums of two-dimensional trigonometric interpolation polynomials. Convergence by Pringsheim for functions of two variables with bounded harmonic variation is established. 相似文献
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Y. Abu Muhanna Rosihan M. Ali Zhen Chuan Ng Siti Farah M. Hasni 《Journal of Mathematical Analysis and Applications》2014
The class consisting of analytic functions f in the unit disk satisfying f+αzf′+γz2f″ subordinated to some function h is considered. The Bohr radius for this class is obtained when h is respectively convex or starlike. The Bohr radius for analytic functions mapping the unit disk into a concave-wedge domain as well as for bounded harmonic mappings are also established. 相似文献
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《Journal of Functional Analysis》1987,72(1):151-181
A definition of a completely bounded multilinear operator from one C1-algebra into another is introduced. Each completely bounded multilinear operator from a C1-algebra into the algebra of bounded linear operators on a Hilbert space is shown to be representable in terms of 1-representations of the C1-algebra and interlacing operators. This result extends Wittstock's Theorem that decomposes a completely bounded linear operator from a C1-algebra into an injective C1-algebra into completely positive linear operators. 相似文献
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Saburou Saitoh 《Proceedings of the American Mathematical Society》1997,125(12):3633-3639
Let be an arbitrary map from an abstract set into an abstract set . We shall use the theory of reproducing kernels to provide a general method for representing the inverse map in terms of . We give several concrete examples of this method.
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Anno Van Streun 《International Journal of Mathematical Education in Science & Technology》2013,44(5):703-725
As part of a large research project—Heuristic Education of Mathematics: developing and investigating strategies to teach applied mathematical problem solving—inquiries were made into the question of the transfer of knowledge and skills from the area of functions to real-world problems. In particular, studies were made of the translation processes from one representation of a problem into another representation. Surprisingly, students often used informal methods not taught in their lessons. After a full year of teaching mathematics, including a lot of applied problem solving, a shift from informal methods to the analytical (expert) solution method was identified. There were also significant differences among the learning results of three instructional design conditions. This research was extended to consider implications of the use of the graphic calculator. Casual use of the graphic calculator diminished the application of analytical methods, but integrated use brought about an enrichment of solution methods. 相似文献
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Marco Thill 《Mathematische Annalen》1989,285(2):297-307
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ABSTRACT In this paper representations of the solutions of all first-order elliptic and hyperbolic systems in three-dimensional and four-dimensional spaces are obtained through the derivatives of harmonic and wave functions, respectively. 相似文献
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B. I. Golubov 《Mathematical Notes》1967,1(3):203-207