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C. J. K. Batty 《Archiv der Mathematik》2003,81(1):72-81
Let $f : \mathbb{R}_{+} \rightarrow \mathbb{C}$ be an exponentially bounded,
measurable function whose Laplace transform has a bounded holomorphic
extension to the open right half-plane. It is known that there is a
constant C such that $\mid \int\limits^t_0 f(s) ds \mid\, \leq C (1 + t)$
for all $t \geq 0$. We show that this estimate is sharp. Furthermore, the
corresponding estimates for orbits of $C_0$-semigroups are also sharp.
Received:17 January 2001; revised manuscropt accepted: 8 February 2001 相似文献
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R. I. Grigorchyuk 《Mathematical Notes》1996,59(4):392-394
It is proved that the singular partH
b
2/(2)
(G) of the second group of bounded homology of the discrete groupG is isomorphic to the space of 2-cocycles that vanish on the diagonal. For groupsG representable as HNN-extensions or free products with amalgamation, as well as for groupsG with one defining relation, conditions for the infinite-dimensionality ofH
b
2/(2)
(G) are found. Some applications of bounded cohomology to the width problem for verbal subgroups and to the boundedness problem
for group presentations are indicated.
Translated fromMatematicheskie Zametki, Vol. 59, No. 4, pp. 546–550, April, 1996.
This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00239. 相似文献
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《Journal of Algebra》1999,211(1):225-239
Given any bounded abelian p-group A for some prime p, we determine a system of representatives for the orbits of A under its automorphism group. This is used to determine the number of orbits. As a consequence, certain types of groups are characterized by this number. 相似文献
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Eberhard Siebert 《manuscripta mathematica》1978,24(2):179-190
Our first theorem is concerned with the convergence of nets of Poisson measures on a topological group. As a corollary we obtain a characterization of Poisson measures. The second theorem gives a characterization of elementary Poisson measures. 相似文献
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Ralph deLaubenfels 《Journal of Mathematical Analysis and Applications》2009,351(1):400-407
We characterize functions u from the real line into a Hilbert space that are the orbits of a unitary group {U(t)}t∈R; that is, u(t)=U(t)u(0), for all real t. One of the characterizations is that u be the Fourier transform of a certain type of vector-valued measure Z; we then use our characterizations to construct Z from u. 相似文献
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O. G. Styrt 《Moscow University Mathematics Bulletin》2010,65(6):255-256
An upper estimate for the codimension of the subspace of points with finite orbits for a representation of a three-dimensional simple compact Lie group whose quotient is a manifold is obtained. 相似文献
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We show that the kernel of an irreducible unitary representation π of the group algebra L1(G) of a completely solvable Lie group G is given by the functions, whose abelian Fourier transform vanish on the Kirillov orbit Oπ of π if and only if this orbit Oπ is flat. This is a generalization of a result obtained before for nilpotent Lie groups. 相似文献
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R. Cushman 《Regular and Chaotic Dynamics》2007,12(6):746-755
In this paper we classify the adjoint orbits of the odd symplectic group over the field of real numbers. We need a noneigenvalue
modulus to classify certain orbits.
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The general construction of frames of p-adic wavelets is described. We consider the orbit of a generic mean zero locally constant function with compact support (mean
zero test function) with respect to the action of the p-adic affine group and show that this orbit is a uniform tight frame. We discuss the relations of this result with the multiresolution
wavelet analysis.
The text was submitted by the authors in English. 相似文献