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1.
Roberto Johnson José Pantoja 《Proceedings of the American Mathematical Society》2007,135(2):579-586
Let be a non-archimedean local field with odd residual characteristic. Let be the group We construct explicit Whittaker models for any supercuspidal representation of with positive level.
2.
In this paper, we give a weak classification of locally linear pseudofree actions of the cyclic group of order on a surface, and prove the existence of such an action which cannot be realized as a smooth action on the standard smooth surface.
3.
K. Smela 《Proceedings of the American Mathematical Society》2007,135(6):1709-1716
We find a condition to be satisfied by strictly increasing sequences of natural numbers guaranteeing that corresponding subsequences of the Haar basis (consisting of full levels) are equivalent or span isomorphic spaces. This applies in particular to Hardy spaces for . We also construct a continuum of greedy nonequivalent bases in .
4.
Yifeng Yu 《Proceedings of the American Mathematical Society》2007,135(5):1449-1454
This note is motivated by Evans (2004) and Anantharaman (2004). We study the semiclassical measure arising from the operator when the potential has degenerate minimum points. We will use the technique of integration by parts and some identities of Evans to derive information on the support of the measure.
5.
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.
6.
Michael A. Hill 《Proceedings of the American Mathematical Society》2007,135(12):4075-4086
In this paper, we introduce a Hopf algebra, developed by the author and André Henriques, which is usable in the computation of the -homology of a space. As an application, we compute the -homology of in a manner analogous to Mahowald and Milgram's computation of the -homology .
7.
For a compact space we consider extending endomorphisms of the algebra to be endomorphisms of Arens-Hoffman and Cole extensions of . Given a non-linear, monic polynomial , with semi-simple, we show that if an endomorphism of extends to the Arens-Hoffman extension with respect to , then it also extends to the simple Cole extension with respect to . We show that the converse to this is false. For a locally connected, metric we characterize the algebraically closed in terms of the extendability of endomorphisms to Arens-Hoffman and to simple Cole extensions.
8.
Takateru Okayasu Yasunori Ueta 《Proceedings of the American Mathematical Society》2007,135(5):1399-1403
We will give some sufficient conditions for a -hyponormal operator, , to be normal, and a sufficient condition for a triplet of operators , , with , self-adjoint and unitary such that necessarily satisfies .
9.
E. Batzies 《Proceedings of the American Mathematical Society》2007,135(10):3341-3347
We establish a homeomorphism between the moduli space of ordered -tuples of 2-dimensional linear subspaces (mod ) and the quotient by simultaneous conjugation of a certain open subset . For , this leads to an explicit computation of the moduli space of central 2-arrangements in mod and its subspace of those classes that contain a complex hyperplane arrangement.
10.
In this paper we consider the existence problem for the elliptic equation on , which arises in the study of conformal deformation of the hyperbolic disc. We prove an existence result for the above equation.
11.
Gregory C. Verchota 《Proceedings of the American Mathematical Society》2007,135(3):891-894
Harmonic maps from the closed disc onto bounded convex sets of the plane obey .
12.
Jerzy Kakol Stephen A. Saxon Aaron R. Todd 《Proceedings of the American Mathematical Society》2004,132(6):1703-1712
Let be a completely regular Hausdorff space, and let be the space of continuous real-valued functions on endowed with the compact-open topology. We find various equivalent conditions for to be a -space, resolving an old question of Jarchow and consolidating work by Jarchow, Mazon, McCoy and Todd. Included are analytic characterizations of pseudocompactness and an example that shows that, for , Grothendieck's -spaces do not coincide with Jarchow's -spaces. Any such example necessarily answers a thirty-year-old question on weak barrelledness properties for , our original motivation.
13.
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 .
14.
Edward M. Fan 《Proceedings of the American Mathematical Society》2008,136(9):3255-3261
Consider an -dimensional smooth Riemannian manifold with a given smooth measure on it. We call such a triple a Riemannian measure space. Perelman introduced a variant of scalar curvature in his recent work on solving Poincaré's conjecture , where and is the scalar curvature of . In this note, we study the topological obstruction for the -stable minimal submanifold with positive -scalar curvature in dimension three under the setting of manifolds with density.
15.
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 .
16.
P. Guerzhoy 《Proceedings of the American Mathematical Society》2007,135(9):2743-2746
The phenomenon of -congruences was recently studied by Ahlgren and Ono (2005) and by Elkies, Ono and Yang (2005). We provide a necessary and sufficient condition which improves their general results.
17.
We study the complexification of real Hilbert -modules over real -algebras. We give an example of a Hilbert -module that is not the complexification of any Hilbert -module, where is a real -algebra.
18.
Robin Harte Young Ok Kim Woo Young Lee 《Proceedings of the American Mathematical Society》2006,134(1):105-110
The spectral pictures of products and of Banach space operators are compared; in particular when one of them is `of index zero'.
19.
Wael Abu-Shammala Alberto Torchinsky 《Proceedings of the American Mathematical Society》2007,135(9):2839-2843
In this paper we present an atomic decomposition of integrable functions. As an application we compute the distance of in to the Hardy space .
20.
Ian M. Aberbach 《Proceedings of the American Mathematical Society》2005,133(1):27-29
Let be an excellent local ring of positive prime characteristic. We show that if , then is regular. This improves a result of Schoutens, in which the additional hypothesis that was an isolated singularity was required for the proof.