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51.
H. Stetkær 《Aequationes Mathematicae》1997,54(1-2):144-172
Summary We produce complete solution formulas of selected functional equations of the formf(x +y) ±f(x + σ (ν)) = Σ
I
2
=1
g
l
(x)h
l
(y),x, y∈G, where the functionsf,g
1,h
1 to be determined are complex valued functions on an abelian groupG and where σ:G→G is an involution ofG. The special case of σ=−I encompasses classical functional equations like d’Alembert’s, Wilson’s first generalization of it, Jensen’s equation and
the quadratic equation. We solve these equations, the equation for symmetric second differences in product form and similar
functional equations for a general involution σ. 相似文献
52.
53.
Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for
the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration
phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper
bounds on spectral gaps.
Received: 10 June 1996 / In revised form: 9 August 1996 相似文献
54.
Kehe Zhu 《Integral Equations and Operator Theory》1998,31(3):371-387
The paper deals with two closely related questions about the Bergman space of the unit disk. First, we investigate a special class of invariant subspaces of the Bergman space, namely, invariant subspaces induced by certain Hankel operators. We show that such spaces always have the co-dimension 1 or 2 property; and we determine exactly when such a space has the co-dimension 1 property. Second, we introduce the notion of inner spaces in the Bergman space and give several characterizations of when an inner space is maximal.Research supported by the National Science Foundation 相似文献
55.
Marianna A. Shubov 《Integral Equations and Operator Theory》1997,28(3):358-372
We announce a series of results on the spectral analysis for a class of nonselfadjoint opeators, which are the dynamics generators for the systems governed by hyperbolic equations containing dissipative terms. Two such equations are considered: the equation of nonhomogeneous damped string and the 3-dimensional damped wave equation with spacially nonhomogeneous spherically symmetric coefficients. Nonselfadjoint boundary conditions are imposed at the ends of a finite interval or on a sphere centered at the origin respectively. Our main result is the fact the aforementioned operators are spectral in the sense of N. Dunford. The result follows from the fact that the systems of root vectors of the above operators form Riesz bases in the corresponding energy spaces. We also give asymptotics of the spectra and state the Riesz basis property results for the nonselfadjoint operator pencils associated with these operators. 相似文献
56.
Kevin Houston 《Inventiones Mathematicae》2002,147(3):471-485
The disentanglement of certain augmentations is shown to be the topological join of a disentanglement and a Milnor fibre.
The kth disentanglement of a finite map is defined and for corank 1 maps from ℂ
n
to ℂ
n
+1 it is shown that they are homotopically equivalent to a wedge of spheres. Applications to the Mond conjecture are given.
Oblatum 24-VII-2000 & 5-VII-2001?Published online: 12 October 2001 相似文献
57.
Robert L. Jerrard Halil Mete Soner 《Calculus of Variations and Partial Differential Equations》2002,14(2):151-191
We study the Ginzburg-Landau functional
for , where U is a bounded, open subset of . We show that if a sequence of functions satisfies , then their Jacobians are precompact in the dual of for every . Moreover, any limiting measure is a sum of point masses. We also characterize the -limit of the functionals , in terms of the function space B2V introduced by the authors in [16,17]: we show that I(u) is finite if and only if , and for is equal to the total variation of the Jacobian measure Ju. When the domain U has dimension greater than two, we prove if then the Jacobians are again precompact in for all , and moreover we show that any limiting measure must be integer multiplicity rectifiable. We also show that the total variation
of the Jacobian measure is a lower bound for the limit of the Ginzburg-Landau functional.
Received: 15 December 2000 / Accepted: 23 January 2001 / Published online: 25 June 2001 相似文献
58.
Several α-ketoalcohols of synthetic value were resolved using lipase as a catalyst. Lipoprotein lipase (LPL) provided the best rate of hydrolysis and kinetic differentiation. One of these optically pure α-ketoalcohol was converted to (5)-ibuprofen in good optical purity. The stereospecific inversion of (R)-alcohol to (S)-alcohol is described. 相似文献
59.
Sans résumé
相似文献
相似文献
60.
Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4]. 相似文献