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1.
Let be a nontrivial dilation. We show that every complete norm on that makes from into itself continuous is equivalent to . also determines the norm of both and with in a weaker sense. Furthermore, we show that even all the dilations do not determine the norm on .
2.
T. Lachand-Robert M. A. Peletier 《Proceedings of the American Mathematical Society》1999,127(6):1723-1727
We investigate the extremal points of a functional , for a convex or concave function . The admissible functions are convex themselves and satisfy a condition . We show that the extremal points are exactly and if these functions are convex and coincide on the boundary . No explicit regularity condition is imposed on , , or . Subsequently we discuss a number of extensions, such as the case when or are non-convex or do not coincide on the boundary, when the function also depends on , etc.
3.
D. A. Redett 《Proceedings of the American Mathematical Society》2005,133(4):1151-1156
In this note we extend the ``Beurling type' characterizations of subspaces of and to and , respectively.
4.
Xingde Dai Yuanan Diao Qing Gu 《Proceedings of the American Mathematical Society》2002,130(6):1661-1667
In this paper we investigate the subspaces of which have normalized tight frame wavelets that are defined by set functions on some measurable subsets of called Bessel sets. We show that a subspace admitting such a normalized tight frame wavelet falls into a class of subspaces called reducing subspaces. We also consider the subspaces of that are generated by a Bessel set in a special way. We present some results concerning the relation between a Bessel set and the corresponding subspace of which either has a normalized tight frame wavelet defined by the set function on or is generated by .
5.
Sandy Grabiner 《Proceedings of the American Mathematical Society》2004,132(6):1675-1684
Suppose that is a weighted convolution algebra on with the weight normalized so that the corresponding space of measures is the dual space of the space of continuous functions. Suppose that is a continuous nonzero homomorphism, where is also a convolution algebra. If is norm dense in , we show that is (relatively) weak dense in , and we identify the norm closure of with the convergence set for a particular semigroup. When is weak continuous it is enough for to be weak dense in . We also give sufficient conditions and characterizations of weak continuity of . In addition, we show that, for all nonzero in , the sequence converges weak to 0. When is regulated, converges to 0 in norm.
6.
S. Prashanth 《Proceedings of the American Mathematical Society》2007,135(1):201-209
Let denote the closure of in the norm Let and define the constants and Let We consider the following problem for We show an exact multiplicity result for for all small .
7.
Madjid Mirzavaziri Mohammad Sal Moslehian 《Proceedings of the American Mathematical Society》2006,134(11):3319-3327
Let be a -algebra acting on a Hilbert space , let be a linear mapping and let be a -derivation. Generalizing the celebrated theorem of Sakai, we prove that if is a continuous -mapping, then is automatically continuous. In addition, we show the converse is true in the sense that if is a continuous --derivation, then there exists a continuous linear mapping such that is a --derivation. The continuity of the so-called - -derivations is also discussed.
8.
Zhiguo Hu 《Proceedings of the American Mathematical Society》2006,134(10):3085-3095
Let be the Fourier algebra of a locally compact group and the -algebra of uniformly continuous linear functionals on . We study how the centre problem for the algebra (resp. ) is related to the centre problem for the algebras (resp. ) of -compact open subgroups of . We extend some results of Lau-Losert on the centres of and .
9.
Tetsuo Nakamura 《Proceedings of the American Mathematical Society》1999,127(6):1589-1595
Let be an elliptic curve over a number field such that
and let denote the number of roots of unity in . Ross proposed a question: Is isogenous over to an elliptic curve such that is cyclic of order dividing ? A counter-example of this question is given. We show that is isogenous to such that . In case has complex multiplication and , we obtain certain criteria whether or not is isogenous to such that .
and let denote the number of roots of unity in . Ross proposed a question: Is isogenous over to an elliptic curve such that is cyclic of order dividing ? A counter-example of this question is given. We show that is isogenous to such that . In case has complex multiplication and , we obtain certain criteria whether or not is isogenous to such that .
10.
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:
11.
Guillaume Aubrun 《Proceedings of the American Mathematical Society》2007,135(5):1293-1303
We prove the following result: for any , only sample points are enough to obtain -approximation of the inertia ellipsoid of an unconditional convex body in . Moreover, for any , already sample points give isomorphic approximation of the inertia ellipsoid. The proofs rely on an adaptation of the moments method from Random Matrix Theory.
12.
YoungJu Choie Winfried Kohnen 《Proceedings of the American Mathematical Society》2003,131(11):3309-3317
The main result of the paper gives an explicit formula for the sum of the values of even order derivatives with respect to of the Weierstrass -function for the lattice (where is in the upper half-plane) extended over the points in the divisor of (where is a meromorphic Jacobi form) in terms of the coefficients of the Laurent expansion of around .
13.
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 .
14.
We introduce the notation for von Neumann algebra II-factors where is allowed to be negative. This notation is defined by rescalings of free products of II-factors, and is proved to be consistent with known results and natural operations. We also give two statements which we prove are equivalent to isomorphism of free group factors.
15.
Karel Dekimpe 《Proceedings of the American Mathematical Society》2003,131(3):973-978
We are dealing with Lie groups which are diffeomorphic to , for some . After identifying with , the multiplication on can be seen as a map . We show that if is a polynomial map in one of the two (sets of) variables or , then is solvable. Moreover, if one knows that is polynomial in one of the variables, the group is nilpotent if and only if is polynomial in both its variables.
16.
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 .
17.
Eberhard Kaniuth Gitta Kutyniok 《Proceedings of the American Mathematical Society》1998,126(12):3561-3569
Let be a locally compact abelian group. The notion of Zak transform on extends to . Suppose that is compactly generated and its connected component of the identity is non-compact. Generalizing a classical result for , we then prove that if is such that its Zak transform is continuous on , then has a zero.
18.
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 .
19.
Marie Choda 《Proceedings of the American Mathematical Society》2006,134(10):2905-2911
Let be the automorphism of the free group which is arising from a permutation of the free generators of The naturally induces the automorphism of the reduced -algebra and also the automorphism of the group factor We show that the Brown-Germain entropy is zero. This implies that the Brown-Voiculescu topological entropy the Connes-Narnhofer-Thirring dynamical entropy and the Connes-Størmer entropy are all zero.
20.
Guia Medolla Alberto G. Setti 《Proceedings of the American Mathematical Society》2000,128(6):1733-1742
Let be a homogeneous tree of degree , , the Laplace operator of and the fundamental solution of the heat equation on . We show that the heat kernel is asymptotically concentrated in an annulus moving to infinity with finite speed . Asymptotic concentration of heat in the norm is also investigated.