共查询到20条相似文献,搜索用时 31 毫秒
1.
Nicolas Burq Andrew Hassell Jared Wunsch 《Proceedings of the American Mathematical Society》2007,135(4):1029-1037
We consider Dirichlet eigenfunctions of the Bunimovich stadium , satisfying . Write where is the central rectangle and denotes the ``wings,' i.e., the two semicircular regions. It is a topic of current interest in quantum theory to know whether eigenfunctions can concentrate in as . We obtain a lower bound on the mass of in , assuming that itself is -normalized; in other words, the norm of is controlled by times the norm in . Moreover, if is an quasimode, the same result holds, while for an quasimode we prove that the norm of is controlled by times the norm in . We also show that the norm of may be controlled by the integral of along , where is a smooth factor on vanishing at . These results complement recent work of Burq-Zworski which shows that the norm of is controlled by the norm in any pair of strips contained in , but adjacent to .
2.
Let be a -group with generator , and let be a local -semigroup commuting with . Then the operators , , form a local -semigroup. It is proved that if is injective and is the generator of , then is closable and is the generator of . Also proved are a characterization theorem for local -semigroups with not necessarily injective and a theorem about solvability of the abstract inhomogeneous Cauchy problem:
3.
Mohsen Pourahmadi Akihiko Inoue Yukio Kasahara 《Proceedings of the American Mathematical Society》2007,135(4):1233-1239
For a nonnegative integrable weight function on the unit circle , we provide an expression for , in terms of the series coefficients of the outer function of , for the weighted distance , where is the normalized Lebesgue measure and ranges over trigonometric polynomials with frequencies in , , . The problem is open for .
4.
Guangxing Zeng 《Proceedings of the American Mathematical Society》2007,135(4):929-938
The purpose of this paper is to investigate the interplay between henselian valuations and orderings (or semiorderings) of a ring. As a main result, it is proved that for a henselian valuation on a ring , the following statements are equivalent: (1) is compatible with every semiordering of ; (2) is compatible with every ordering of ; (3) Every real prime ideal of is contained in the core of .
5.
David Schrittesser 《Proceedings of the American Mathematical Society》2007,135(4):1213-1222
-absoluteness for forcing means that for any forcing , . `` inaccessible to reals' means that for any real , . To measure the exact consistency strength of `` -absoluteness for forcing and is inaccessible to reals', we introduce a weak version of a weakly compact cardinal, namely, a (lightface) -indescribable cardinal; has this property exactly if it is inaccessible and .
6.
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 .
7.
Sté phane R. Louboutin Joë l Rivat Andrá s Sá rkö zy 《Proceedings of the American Mathematical Society》2007,135(4):969-975
Let be an odd prime number. For we denote the inverse of modulo by with . Given , we prove that in any range of length the probability that has the same parity as tends to as . This result was previously known only to hold true in the full range of length . We will also obtain quantitative results on the pseudorandomness of the sequence for which we estimate the well-distribution and correlation measures as defined by Mauduit and Sárközy (1997).
8.
Given a perfect field of characteristic , a smooth proper -scheme , a crystal on relative to and a finite group acting on and , we show that, viewed as a virtual -module, the reduction modulo of the crystalline cohomology of is the de Rham cohomology of modulo . On the way we prove a base change theorem for the virtual -representations associated with -equivariant objects in the derived category of -modules.
9.
Albin L. Jones 《Proceedings of the American Mathematical Society》2007,135(4):1197-1204
Consider an arbitrary partition of the triples of all countable ordinals into two classes. We show that either for each finite ordinal the first class of the partition contains all triples from a set of type , or for each finite ordinal the second class of the partition contains all triples of an -element set. That is, we prove that for each pair of finite ordinals and .
10.
Henrik Petersson 《Proceedings of the American Mathematical Society》2007,135(4):1145-1149
A sequence of operators is said to be hypercyclic if there exists a vector , called hypercyclic for , such that is dense. A hypercyclic subspace for is a closed infinite-dimensional subspace of, except for zero, hypercyclic vectors. We prove that if is a sequence of operators on that has a hypercyclic subspace, then there exist (i) a sequence of one variable polynomials such that is hypercyclic for every fixed and (ii) an operator that maps nonzero vectors onto hypercyclic vectors for .
We complement earlier work of several authors.
11.
Bruce A. Barnes 《Proceedings of the American Mathematical Society》2007,135(6):1735-1740
Let be a bounded linear operator on a Banach space and let be a subspace of which is a Banach space and invariant. Denote by the restriction of to This paper explores the questions:
If the range of is closed, under what conditions is the range of closed?
If the range of is closed, under what conditions is the range of closed?
12.
Benjamin D. Miller Christian Rosendal 《Proceedings of the American Mathematical Society》2007,135(2):517-522
Suppose that and are Polish groups which act in a Borel fashion on Polish spaces and . Let and denote the corresponding orbit equivalence relations, and and the corresponding Borel full groups. Modulo the obvious counterexamples, we show that .
13.
S. Rohde 《Proceedings of the American Mathematical Society》2007,135(4):1169-1173
In this note, we provide an answer to a question of D. Mejia and Chr. Pommerenke, by constructing a hyperbolically convex subdomain of the unit disc so that the conformal map from to maps a set of dimension 0 on to a set of dimension
14.
Let be an -dimensional space of linear operators between the linear spaces and over an algebraically closed field . Improving results of Larson, Ding, and Li and Pan we show the following.
Theorem. Let be a basis of . Assume that every nonzero operator in has rank larger than . Then a linear operator belongs to if and only if for every , is a linear combination of .
15.
Walter Ferrer Santos Alvaro Rittatore 《Proceedings of the American Mathematical Society》2007,135(4):961-968
In this paper we axiomatize some constructions and results due to Cayley and Hilbert. We define the concept of -process for an arbitrary affine algebraic monoid with zero and unit group . In our situation we show how to produce from the process and for a linear rational representation of a number of elements of the ring of -invariants that is large enough to guarantee its finite generation. Moreover, using complete reducibility, we give an explicit construction of all -processes for reductive monoids.
16.
Let be the set of all linear transformations from to , where and are vector spaces over a field . We show that every -dimensional subspace of is algebraically -reflexive, where denotes the largest integer not exceeding , provided is less than the cardinality of .
17.
Florin Panaite Freddy Van Oystaeyen 《Proceedings of the American Mathematical Society》2007,135(6):1669-1677
If is a quasi-Hopf algebra and is a right -comodule algebra such that there exists a morphism of right -comodule algebras, we prove that there exists a left -module algebra such that . The main difference when comparing to the Hopf case is that, from the multiplication of , which is associative, we have to obtain the multiplication of , which in general is not; for this we use a canonical projection arising from the fact that becomes a quasi-Hopf -bimodule.
18.
For spaces on , and , sharp versions of the classical Marchaud inequality are known. These results are extended here to Orlicz spaces (on , and ) for which is convex for some , , where is the Orlicz function. Sharp converse inequalities for such spaces are deduced.
19.
Margarida Mendes Lopes Rita Pardini 《Proceedings of the American Mathematical Society》2007,135(5):1279-1282
In this note it is shown that, given a smooth minimal complex surface of general type with , , for which the bicanonical map is a morphism, the degree of is not 3. This completes our earlier results, showing that if is a minimal surface of general type with , such that is free, then the bicanonical map of can have degree 1, 2 or 4.
20.
Mariagrazia Bianchi David Chillag Mark L. Lewis Emanuele Pacifici 《Proceedings of the American Mathematical Society》2007,135(3):671-676
Let be a finite group, and write for the set of degrees of irreducible characters of . We define to be the graph whose vertex set is , and there is an edge between and if . We prove that if is a complete graph, then is a solvable group.