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1.
Fabio Nicola 《Proceedings of the American Mathematical Society》2003,131(9):2841-2848
We are concerned with the so-called -pseudo-differential calculus. We describe the spectrum of the unital and commutative -algebra given by the norm closure of the space of -order pseudo-differential operators modulo compact operators; other related algebras are also considered. Finally, their -theory is computed.
2.
Ariel Pacetti Fernando Rodriguez Villegas with an appendix by B. Gross. 《Mathematics of Computation》2005,74(251):1545-1557
For a prime we describe an algorithm for computing the Brandt matrices giving the action of the Hecke operators on the space of modular forms of weight and level . For we define a special Hecke stable subspace of which contains the space of modular forms with CM by the ring of integers of and we describe the calculation of the corresponding Brandt matrices.
3.
M. M. Popov 《Proceedings of the American Mathematical Society》2005,133(7):2023-2028
Let p_1 > p_2 > \cdots > 1$">. We construct an easily determined -symmetric basic sequence in , which spans a hereditarily subspace without the Schur property. An immediate consequence is the existence of hereditarily subspaces of without the Schur property.
4.
Andreas Weingartner 《Proceedings of the American Mathematical Society》2007,135(9):2677-2681
Let be the sum of the positive divisors of . We show that the natural density of the set of integers satisfying is given by , where denotes Euler's constant. The same result holds when is replaced by , where is Euler's totient function.
5.
Adam S. Sikora 《Transactions of the American Mathematical Society》2005,357(5):2007-2020
We investigate the relations between the cut number, and the first Betti number, of -manifolds We prove that the cut number of a ``generic' -manifold is at most This is a rather unexpected result since specific examples of -manifolds with large and are hard to construct. We also prove that for any complex semisimple Lie algebra there exists a -manifold with and Such manifolds can be explicitly constructed.
6.
Suppose that is a smooth -action on a closed smooth -dimensional manifold such that all Stiefel-Whitney classes of the tangent bundle to each connected component of the fixed point set vanish in positive dimension. This paper shows that if 2^k\dim F$"> and each -dimensional part possesses the linear independence property, then bounds equivariantly, and in particular, is the best possible upper bound of if is nonbounding.
7.
Siddhartha Gadgil 《Proceedings of the American Mathematical Society》2004,132(12):3705-3714
We show that an oriented elliptic -manifold admits a universally tight positive contact structure if and only if the corresponding group of deck transformations on (after possibly conjugating by an isometry) preserves the standard contact structure.
We also relate universally tight contact structures on -manifolds covered by to the isomorphism .
The main tool used is equivariant framings of -manifolds.
8.
Stefano Meda Peter Sjö gren Maria Vallarino 《Proceedings of the American Mathematical Society》2008,136(8):2921-2931
We prove that if is in , is a Banach space, and is a linear operator defined on the space of finite linear combinations of -atoms in with the property that then admits a (unique) continuous extension to a bounded linear operator from to . We show that the same is true if we replace -atoms by continuous -atoms. This is known to be false for -atoms.
9.
Michael J. Fisher 《Proceedings of the American Mathematical Society》2003,131(11):3617-3621
Let be a fixed odd prime. In this paper we prove an exponent conjecture of Bousfield, namely that the -exponent of the spectrum is for . It follows from this result that the -exponent of is at least for and , where denotes the -connected cover of .
10.
Fernando Szechtman 《Proceedings of the American Mathematical Society》2003,131(12):3657-3664
We refer to an automorphism of a group as -inner if given any subset of with cardinality less than , there exists an inner automorphism of agreeing with on . Hence is 2-inner if it sends every element of to a conjugate. New examples are given of outer -inner automorphisms of finite groups for all natural numbers .
11.
Assaf Naor 《Transactions of the American Mathematical Society》2007,359(3):1045-1079
We prove a concentration inequality for the norm on the sphere for . This inequality, which generalizes results of Schechtman and Zinn (2000), is used to study the distance between the cone measure and surface measure on the sphere of . In particular, we obtain a significant strengthening of the inequality derived by Naor and Romik (2003), and calculate the precise dependence of the constants that appeared there on .
12.
Manuel Blickle 《Transactions of the American Mathematical Society》2003,355(4):1647-1668
Let be a regular ring, essentially of finite type over a perfect field . An -module is called a unit -module if it comes equipped with an isomorphism , where denotes the Frobenius map on , and is the associated pullback functor. It is well known that then carries a natural -module structure. In this paper we investigate the relation between the unit -structure and the induced -structure on . In particular, it is shown that if is algebraically closed and is a simple finitely generated unit -module, then it is also simple as a -module. An example showing the necessity of being algebraically closed is also given.
13.
John T. Anderson Alexander J. Izzo John Wermer 《Proceedings of the American Mathematical Society》2004,132(5):1495-1500
We prove: Let be a compact real-analytic variety in . Assume (i) is polynomially convex and (ii) every point of is a peak point for . Then . This generalizes a previous result of the authors on polynomial approximation on three-dimensional real-analytic submanifolds of .
14.
Sergei V. Astashkin Lech Maligranda 《Proceedings of the American Mathematical Society》2004,132(10):2929-2938
We show that if is a rearrangement invariant space on that is an interpolation space between and and for which we have only a one-sided estimate of the Boyd index 1/p, 1 < p < \infty$">, then is an interpolation space between and . This gives a positive answer for a question posed by Semenov. We also present the one-sided interpolation theorem about operators of strong type and weak type .
15.
R. Dante DeBlassie Pedro J. Mé ndez-Herná ndez 《Transactions of the American Mathematical Society》2007,359(5):2343-2359
Let be a domain of finite Lebesgue measure in and let be the symmetric -stable process killed upon exiting . Each element of the set of eigenvalues associated to , regarded as a function of , is right continuous. In addition, if is Lipschitz and bounded, then each is continuous in and the set of associated eigenfunctions is precompact.
16.
John L. Simons. 《Mathematics of Computation》2005,74(251):1565-1572
This article generalizes a proof of Steiner for the nonexistence of -cycles for the problem to a proof for the nonexistence of -cycles. A lower bound for the cycle length is derived by approximating the ratio between numbers in a cycle. An upper bound is found by applying a result of Laurent, Mignotte, and Nesterenko on linear forms in logarithms. Finally numerical calculation of convergents of shows that -cycles cannot exist.
17.
Muharem Avdispahic Lejla Smajlovic 《Proceedings of the American Mathematical Society》2006,134(7):2125-2130
A. Magyar's result on -bounds for a family of operators on -spheres () in is improved to match the corresponding theorem for -spheres.
18.
Let be a random -CNF formula formed by selecting uniformly and independently out of all possible -clauses on variables. It is well known that if , then is unsatisfiable with probability that tends to 1 as . We prove that if , where , then is satisfiable with probability that tends to 1 as .
Our technique, in fact, yields an explicit lower bound for the random -SAT threshold for every . For our bounds improve all previously known such bounds.
19.
Brian Harbourne Sandeep Holay Stephanie Fitchett 《Transactions of the American Mathematical Society》2003,355(2):593-608
The notion of a quasiuniform fat point subscheme is introduced and conjectures for the Hilbert function and minimal free resolution of the ideal defining are put forward. In a large range of cases, it is shown that the Hilbert function conjecture implies the resolution conjecture. In addition, the main result gives the first determination of the resolution of the th symbolic power of an ideal defining general points of when both and are large (in particular, for infinitely many for each of infinitely many , and for infinitely many for every 2$">). Resolutions in other cases, such as ``fat points with tails', are also given. Except where an explicit exception is made, all results hold for an arbitrary algebraically closed field . As an incidental result, a bound for the regularity of is given which is often a significant improvement on previously known bounds.
20.
Rü diger Gö bel Warren May 《Proceedings of the American Mathematical Society》2003,131(10):2987-2992
Under the assumptions of MA and CH, it is proved that if is a field of prime characteristic and is an -separable abelian -group of cardinality , then an isomorphism of the group algebras and implies an isomorphism of and .