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81.
A nonlinear integral operator T of the form (Tf)(s)=∫G K(t, f (σ(s, t))) dμ(t), for sG, is defined and investigated in the measure space (G, Σ, μ), where f and K are vector-valued functions with values in normed linear spaces E and F, respectively. The results are applied to the case of integro-differential operators in generalized Orlicz–Sobolev spaces. There are studied problems of existence, embeddings, and approximation by means of T. 相似文献
82.
Jasper V. Stokman 《Transactions of the American Mathematical Society》2000,352(4):1527-1579
The five parameter family of Koornwinder's multivariable analogues of the Askey-Wilson polynomials is studied with four parameters generically complex. The Koornwinder polynomials form an orthogonal system with respect to an explicit (in general complex) measure. A partly discrete orthogonality measure is obtained by shifting the contour to the torus while picking up residues. A parameter domain is given for which the partly discrete orthogonality measure is positive. The orthogonality relations and norm evaluations for multivariable -Racah polynomials and multivariable big and little -Jacobi polynomials are proved by taking suitable limits in the orthogonality relations for the Koornwinder polynomials. In particular new proofs of several well-known -analogues of the Selberg integral are obtained.
83.
We associate a family of Hilbert spaces H
q
2;(D) of analytic functions on the unit disk D=z
:|z|<1 the q-continuous Gegenbauer polynomials C
n
(x;q) on the interval]–1;1[ and give a q-analogue of the unitary integral transform that Watanabe constructed from the Hilbert space L
2(]–1;1[;(1–x
2)–
dx onto the weighted Hilbert space H
2;(D). 相似文献
84.
罗群 《数学的实践与认识》2013,43(3)
给出了函数的平均值问题的良定性概念,并证明了有界闭区间上连续函数的平均值问题是G-wp和GLP-wp的等结论. 相似文献
85.
Hong Hai Liu 《数学学报(英文版)》2012,28(11):2227-2242
In this paper, the author studies the mapping properties for some general maximal operators and singular integrals on certain function spaces via Fourier transform estimates. Also, some concrete maximal operators and singular integrals are studied as applications. 相似文献
86.
J.M. Melenk 《Journal of Computational and Applied Mathematics》2010,234(6):1692-1701
We analyze the convergence behavior of Filon-type quadrature rules by making explicit the dependence on both k, the parameter that controls the oscillatory behavior of the integrand, and n, the number of function evaluations. We provide explicit conditions on the domain of analyticity of the integrand to ensure convergence for n→∞. 相似文献
87.
Leslie C. Cheng 《数学学报(英文版)》2008,24(6):1031-1038
We establish the L^p boundedness of Marcinkiewicz integral operators with kernels in theHardy space on a compact submanifold of finite type. Previously such boundedness properties were obtained when the submanifold is a sphere. Our result shows that what matters is not the symmetry, but a certain type of curvature property of the submanifold. 相似文献
88.
Simplified expressions for one-centre electron interaction integrals in general and Slater-Condon parameters as well as repulsion
integrals of the type (aa|aa) in particular have been obtained over Slater-type atomic orbitals. Results calculated using these expressions are in agreement
with those due to other authors. 相似文献
89.
In this article we shall determine the automorphic integrals of positive and negative integral weight associated with the full modular group and some Hecke groups. This will be done by using the Hecke Correspondence. We will also give a characterization of multiplier systems of real weight for Hecke groups. 相似文献
90.
Kirkwood–Buff (K–B) integrals play an important role in characterizing the properties and interactions of various liquid mixtures. However, there exists no method to calculate directly the K–B integrals from the easily available experimental data of ultrasonic velocity and density. An attempt has been made to evaluate the same using these initial parameters. A statistical mechanical theory advanced by Arakawa et al. has been used here, in combination with a semi-empirical formula to compute K–B parameters in the whole concentration range for six binary systems at atmospheric pressure and at 298.15 K. 相似文献