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11.
Yakov Varshavsky 《Geometric And Functional Analysis》2007,17(1):271-319
The goal of this paper is to generalize a theorem of Fujiwara (Deligne’s conjecture) to the situation appearing in a joint
work [KV] with David Kazhdan on the global Langlands correspondence over function fields. Moreover, our proof is more elementary
than the original one and stays in the realm of ordinary algebraic geometry, that is, does not use rigid geometry. We also
give a proof of the Lefschetz–Verdier trace formula and of the additivity of filtered trace maps, thus making the paper essentially
self-contained.
The work was supported by the Israel Science Foundation (Grant No. 555/04)
Received: May 2005 Accepted: August 2005 相似文献
12.
本文运用复变函数论中的Rouche定理,对Person不可约方法作了大的改进,一系列多项式的不可约性被证实. 相似文献
13.
Rajesh Pereira 《Journal of Mathematical Analysis and Applications》2003,285(1):336-348
In 1959, Davis introduced the concept of a differentiator of an operator on a finite-dimensional Hilbert space. We prove that every such operator possesses a differentiator. We also use the theory of differentiators to solve several problems in the geometry of polynomials. For instance, we answer in the affirmative a twenty year old unsolved conjecture of Schoenberg, a related conjecture of Katsoprinakis and a fifty year old unsolved conjecture of De Bruijn and Springer. 相似文献
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We quantify the long-time behavior of solutions to the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell molecules by means of the contraction property of a suitable metric in the set of probability measures. Existence, uniqueness, and precise estimates of overpopulated high energy tails of the self-similar profile proved in ref. 9 are revisited and derived from this new Liapunov functional. For general initial conditions the solutions of the Boltzmann equation are then proved to converge with computable rate as t → ∞ to the self-similar solution in this distance, which metrizes the weak convergence of measures. Moreover, we can relate this Fourier distance to the Euclidean Wasserstein distance or Tanaka functional proving also its exponential convergence towards the homogeneous cooling states. The findings are relevant in the understanding of the conjecture formulated by Ernst and Brito in refs. 15, 16, and complement and improve recent studies on the same problem of Bobylev and Cercignani(9) and Bobylev, Cercignani and one of the authors.(11) 相似文献
17.
S. R. Nasyrov 《Mathematical Notes》2007,82(5-6):798-802
We consider functions f that are univalent in a plane angular domain of angle απ, 0 < α ≤ 2. It is proved that there exists a natural number k depending only on α such that the kth derivatives f (k) of these functions cannot be univalent in this angle. We find the least of the possible values of for k. As a consequence, we obtain an answer to the question posed by Kir’yatskii: if f is univalent in the half-plane, then its fourth derivative cannot be univalent in this half-plane. 相似文献
18.
An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb. 相似文献
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20.
Peter G. Casazza Ole Christensen Alexander M. Lindner Roman Vershynin 《Proceedings of the American Mathematical Society》2005,133(4):1025-1033
We show that the conjectured generalization of the Bourgain-Tzafriri restricted-invertibility theorem is equivalent to the conjecture of Feichtinger, stating that every bounded frame can be written as a finite union of Riesz basic sequences. We prove that any bounded frame can at least be written as a finite union of linearly independent sequences. We further show that the two conjectures are implied by the paving conjecture. Finally, we show that Weyl-Heisenberg frames over rational lattices are finite unions of Riesz basic sequences.