共查询到20条相似文献,搜索用时 283 毫秒
1.
Dennis Courtney Paul S. Muhly Samuel W. Schmidt 《Complex Analysis and Operator Theory》2012,6(1):163-188
If b is an inner function, then composition with b induces an endomorphism, β, of
L¥(\mathbbT){L^\infty({\mathbb{T}})} that leaves
H¥(\mathbbT){H^\infty({\mathbb{T}})} invariant. We investigate the structure of the endomorphisms of
B(L2(\mathbbT)){B(L^2({\mathbb{T}}))} and
B(H2(\mathbbT)){B(H^2({\mathbb{T}}))} that implement β through the representations of
L¥(\mathbbT){L^\infty({\mathbb{T}})} and
H¥(\mathbbT){H^\infty({\mathbb{T}})} in terms of multiplication operators on
L2(\mathbbT){L^2({\mathbb{T}})} and
H2(\mathbbT){H^2({\mathbb{T}})} . Our analysis, which is based on work of Rochberg and McDonald, will wind its way through the theory of composition operators
on spaces of analytic functions to recent work on Cuntz families of isometries and Hilbert C*-modules. 相似文献
2.
T. Nakazi 《Archiv der Mathematik》1999,73(6):439-441
Let a\alpha and b\beta be bounded measurable functions on the unit circle T. The singular integral operator Sa, bS_{\alpha ,\,\beta } is defined by Sa, b f = aPf + bQf(f ? L2 (T))S_{\alpha ,\,\beta } f = \alpha Pf + \beta Qf(f \in L^2 (T)) where P is an analytic projection and Q is a co-analytic projection. In the previous paper, the norm of Sa, bS_{\alpha ,\,\beta } was calculated in general, using a,b\alpha ,\beta and a[`(b)] + H¥\alpha \bar {\beta } + H^\infty where H¥H^\infty is a Hardy space in L¥ (T).L^\infty (T). In this paper, the essential norm ||Sa, b ||e\Vert S_{\alpha ,\,\beta } \Vert _e of Sa, bS_{\alpha ,\,\beta } is calculated in general, using a[`(b)] + H¥ + C\alpha \bar {\beta } + H^\infty + C where C is a set of all continuous functions on T. Hence if a[`(b)]\alpha \bar {\beta } is in H¥ + CH^\infty + C then ||Sa, b ||e = max(||a||¥ , ||b||¥ ).\Vert S_{\alpha ,\,\beta } \Vert _e = \max (\Vert \alpha \Vert _\infty , \Vert \beta \Vert _\infty ). This gives a known result when a, b\alpha , \beta are in C. 相似文献
3.
The large time behaviour of the Lq L^q -norm of nonnegative solutions to the "anisotropic" viscous Hamilton-Jacobi equation¶¶
ut - Du + ?i=1m |uxi|pi = 0 in \mathbbR+×\mathbbRN,u_t - \Delta u + \sum_{i=1}^m \vert u_{x_i}\vert^{p_i} = 0 \;\;\mbox{ in }\; {\mathbb{R}}_+\times{\mathbb{R}}^N,¶¶is studied for q=1 q=1 and q=¥ q=\infty , where m ? {1,?,N} m\in\{1,\ldots,N\} and pi ? [1,+¥) p_i\in [1,+\infty) for i ? {1,?,m} i\in\{1,\ldots,m\} . The limit of the L1 L^1 -norm is identified, and temporal decay estimates for the L¥ L^\infty -norm are obtained, according to the values of the pi p_i 's. The main tool in our approach is the derivation of L¥ L^\infty -decay estimates for ?(ua ), a ? (0,1] \nabla\left(u^\alpha \right), \alpha\in (0,1] , by a Bernstein technique inspired by the ones developed by Bénilan for the porous medium equation. 相似文献
4.
Rolf Farnsteiner 《Archiv der Mathematik》1999,72(1):28-39
Let (L,[p]) a finite dimensional nilpotent restricted Lie algebra of characteristic p 3 3, c ? L*p \geq 3, \chi \in L^* a linear form. In this paper we study the representation theory of the reduced universal enveloping algebra u(L,c)u(L,\chi ). It is shown that u(L,c)u(L,\chi ) does not admit blocks of tame representation type. As an application, we prove that the nonregular AR-components of u(L,c)u(L,\chi ) are of types \Bbb Z [A¥ ]\Bbb Z [A_\infty ] or \Bbb Z [An]/(t)\Bbb Z [A_n]/(\tau ). 相似文献
5.
Alberto Farina 《Monatshefte für Mathematik》2003,179(2):265-269
(w, c) ? R2, u ? Lloc3 (RN, C)\font\Opr=msbm10 at 8pt \def\Op#1{\hbox{\Opr{#1}}}(\omega, c)\in {\Op R}^2, {\upsilon} \in L_{\rm loc}^3 ({\Op R}^N, {\bf C}) and x||j||L¥(RN×R)2 £ max{0, 1-w+[(c2)/4]}.\font\Opr=msbm10 at 8pt \def\Op#1{\hbox{\Opr{#1}}}\Vert\varphi\Vert_{L^\infty({\Op R}^N\times{\Op R})}^2 \le \max\bigg\{0, 1-\omega+{c^2\over 4}\bigg\}. 相似文献
6.
M. M. Santos 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2002,161(1):661-675
We consider the boundary value problem for the stationary Navier-Stokes equations describing an inhomogeneous incompressible fluid in a two dimensional bounded domain. We show the existence of a weak solution with boundary values for the density prescribed in L¥L^{\infty}. 相似文献
7.
In this paper we study the existence of a solution in ${L^\infty_{\rm loc}(\Omega)}In this paper we study the existence of a solution in L¥loc(W){L^\infty_{\rm loc}(\Omega)} to the Euler–Lagrange equation for the variational problem
inf[`(u)] + W1,¥0(W) òW (ID(?u) + g(u)) dx, (0.1)\inf_{\bar u + W^{1,\infty}_0(\Omega)} \int\limits_{\Omega} ({\bf I}_D(\nabla u) + g(u)) dx,\quad \quad \quad \quad \quad(0.1) 相似文献
8.
E. Decreux 《Archiv der Mathematik》2000,75(6):430-437
In this note, we examine the structure of closed ideals of a quasianalytic weighted Beurling algebra A\cal {A}. This algebra is contained in C¥ (G){\cal C}^\infty (\mit\Gamma) and contains the set A¥ (D)A^\infty (D). Like in a previous article (see [6]), we use division properties and we give a characterization of closed ideals I such that I?A¥ 1 { 0}I\cap A^\infty\! \ne \{ 0\} . Then, we use a factorization property proved in [2], which allows us to describe all the closed ideals of A\cal {A}. 相似文献
9.
D. Walsh 《Archiv der Mathematik》1999,73(6):442-458
Suppose that $1 < p < \infty $1 < p < \infty , q=p/(p-1)q=p/(p-1), and for non-negative f ? Lp(-¥ ,¥)f\in L^p(-\infty\! ,\infty ) and any real x we let F(x)-F(0)=ò0xf(t) dtF(x)-F(0)=\int _0^xf(t)\ dt; suppose in addition that ò-¥¥ F(t)exp(-|t|) dt=0\int\limits _{-\infty }^\infty F(t)\exp (-|t|)\ dt=0. Moser's second one-dimensional inequality states that there is a constant CpC_p, such that ò-¥¥ exp[a |F(x)|q-|x|] dx £ Cp\int\limits _{-\infty }^\infty \exp [a |F(x)|^q-|x|] \ dx\le C_p for each f with ||f||p £ 1||f||_p\le 1 and every a £ 1a\le 1. Moreover the value a = 1 is sharp. We replace the operation connecting f with F by a more general integral operation; specifically we consider non-negative kernels K(t,x) with the property that xK(t,x) is homogeneous of degree 0 in t, x. We state an analogue of the inequality above for this situation, discuss some applications and consider the sharpness of the constant which replaces a. 相似文献
10.
S. Bhargava M. S. Mahadeva Naika M. C. Maheshkumar 《Ukrainian Mathematical Journal》2009,61(8):1233-1249
We obtain a modular transformation for the theta function
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