共查询到20条相似文献，搜索用时 0 毫秒
1.
Allan J. Silberger 《Transactions of the American Mathematical Society》1996,348(11):4673-4686
Let be a reductive -adic group. In his paper, ``The Plancherel Formula for Reductive -adic Groups", Harish-Chandra summarized the theory underlying the Plancherel formula for and sketched a proof of the Plancherel theorem for . One step in the proof, stated as Theorem 11 in Harish-Chandra's paper, has seemed an elusively difficult step for the reader to supply. In this paper we prove the Plancherel theorem, essentially, by proving a special case of Theorem 11. We close by deriving a version of Theorem 11 from the Plancherel theorem.
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In this paper, we mainly investigate the $mathfrak{X}$-Gorenstein projective dimension of modules and the (left) $mathfrak{X}$-Gorenstein global dimension of rings. Some properties of $mathfrak{X}$-Gorenstein projective dimensions are obtained. Furthermore, we prove that the (left) $mathfrak{X}$-Gorenstein global dimension of a ring $R$ is equal to the supremum of the set of $mathfrak{X}$-Gorenstein projective dimensions of all cyclic (left) $R$-modules. This result extends the well-known Auslander's theorem on the global dimension and its Gorenstein homological version. 相似文献
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先给出了Schwartz空间的标准半范数族的一个等价的范数族,然后给出了缓增分布表示的一个直接证明. 相似文献
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Soon-Yeong Chung Dohan Kim Sungjin Lee 《Proceedings of the American Mathematical Society》1997,125(11):3229-3234
We give an elementary proof of the equivalence of the original definition of Schwartz and our characterization for the Schwartz space . The new proof is based on the Landau inequality concerning the estimates of derivatives. Applying the same method, as an application, we give a better symmetric characterization of the Beurling-Björck space of test functions for tempered ultradistributions with respect to Fourier transform without conditions on derivatives.
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For a connected linear semisimple Lie group , this paper considers those nonzero limits of discrete series representations having infinitesimal character 0, calling them totally degenerate. Such representations exist if and only if has a compact Cartan subgroup, is quasisplit, and is acceptable in the sense of Harish-Chandra.
Totally degenerate limits of discrete series are natural objects of study in the theory of automorphic forms: in fact, those automorphic representations of adelic groups that have totally degenerate limits of discrete series as archimedean components correspond conjecturally to complex continuous representations of Galois groups of number fields. The automorphic representations in question have important arithmetic significance, but very little has been proved up to now toward establishing this part of the Langlands conjectures.
There is some hope of making progress in this area, and for that one needs to know in detail the representations of under consideration. The aim of this paper is to determine the classification parameters of all totally degenerate limits of discrete series in the Knapp-Zuckerman classification of irreducible tempered representations, i.e., to express these representations as induced representations with nondegenerate data.
The paper uses a general argument, based on the finite abelian reducibility group attached to a specific unitary principal series representation of . First an easy result gives the aggregate of the classification parameters. Then a harder result uses the easy result to match the classification parameters with the representations of under consideration in representation-by-representation fashion. The paper includes tables of the classification parameters for all such groups .
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XI NanHua 《中国科学 数学(英文版)》2014,57(6):1109-1120
In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps. 相似文献
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E. G. Kwon 《Proceedings of the American Mathematical Society》1996,124(5):1473-1480
If is a holomorphic self-map of the open unit disc and , then the following are equivalent. for all Bloch functions .
where is the hyperbolic derivative of : .
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Alexander Shibakov 《Proceedings of the American Mathematical Society》1996,124(8):2599-2607
Using CH we construct a countable sequential topological group whose sequential order is between and giving a consistent negative answer to P. Niykos' question.
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Rauno Aulaskari Hasi Wulan Ruhan Zhao 《Proceedings of the American Mathematical Society》2000,128(8):2329-2335
For let be the Möbius transformation defined by , and let be the Green's function of the unit disk . We construct an analytic function belonging to for all , , but not belonging to meromorphic in and for any , . This gives a clear difference as compared to the analytic case where the corresponding function spaces ( and ) are same.
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Alexander Shibakov 《Proceedings of the American Mathematical Society》1998,126(3):943-947
We prove that a Hausdorff sequential topological group with a point-countable -network is metrizable iff its sequential order is less than . In the non Hausdorff case metrizability may be replaced by -locally finite base.
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Mihai N. Pascu 《Proceedings of the American Mathematical Society》2005,133(6):1707-1711
We use Lévy's theorem on invariance of planar Brownian motion under conformal maps and the support theorem for Brownian motion to show that the range of a non-constant polynomial of a complex variable consists of the whole complex plane. In particular, we obtain a probabilistic proof of the fundamental theorem of algebra.
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A. V. Stoyanovskii 《Functional Analysis and Its Applications》2006,40(3):241-243
We describe the image of the Weil representation of the double covering of the symplectic group in the Schwartz space in the so-called geometric realization, i.e., in holomorphic functions on the symmetric domain called the Siegel upper half-plane. 相似文献
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B. P. Duggal 《Proceedings of the American Mathematical Society》2007,135(9):2899-2905
A Banach space operator is completely hereditarily normaloid, , if either every part, and (also) for every invertible part , of is normaloid or if for every complex number every part of is normaloid. Sufficient conditions for the perturbation of by an algebraic operator to satisfy Weyl's theorem are proved. Our sufficient conditions lead us to the conclusion that the conjugate operator satisfies -Weyl's theorem.
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We present a general approach to derive sampling theorems on locally compact groups from oscillation estimates. We focus on the L
2-stability of the sampling operator by using notions from frame theory. This approach yields particularly simple and transparent reconstruction procedures. We then apply these methods to the discretization of discrete series representations and to Paley–Wiener spaces on stratified Lie groups. 相似文献
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Francesca Astengo 《Journal of Functional Analysis》2009,256(5):1565-2814
Let Hn be the (2n+1)-dimensional Heisenberg group and K a compact group of automorphisms of Hn such that (K?Hn,K) is a Gelfand pair. We prove that the Gelfand transform is a topological isomorphism between the space of K-invariant Schwartz functions on Hn and the space of Schwartz function on a closed subset of Rs homeomorphic to the Gelfand spectrum of the Banach algebra of K-invariant integrable functions on Hn. 相似文献
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Elijah Liflyand Ferenc Mó ricz 《Proceedings of the American Mathematical Society》2000,128(5):1391-1396
We prove that the Hausdorff operator generated by a function is bounded on the real Hardy space . The proof is based on the closed graph theorem and on the fact that if a function in is such that its Fourier transform equals for (or for ), then .
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Guillermo P. Curbera;Susumu Okada;Werner J. Ricker; 《Mathematische Nachrichten》2024,297(10):3927-3942
The finite Hilbert transform T$T$, when acting in the classical Zygmund space LlogL$Ltextnormal {log} L$ (over (−1,1)$(-1,1)$), was intensively studied in [8]. In this note, an integral representation of T$T$ is established via the L1(−1,1)$L^1(-1,1)$-valued measure mL1:A↦T(χA)$m_{L^1}: Amapsto T(chi _A)$ for each Borel set A⊆(−1,1)$Asubseteq (-1,1)$. This integral representation, together with various non-trivial properties of mL1$m_{L^1}$, allows the use of measure theoretic methods (not available in [8]) to establish new properties of T$T$. For instance, as an operator between Banach function spaces T$T$ is not order bounded, it is not completely continuous and neither is it weakly compact. An appropriate Parseval formula for plays a crucial role. 相似文献