共查询到20条相似文献,搜索用时 15 毫秒
1.
Michael Ruzhansky 《Archiv der Mathematik》1999,72(1):68-76
We will show that the factorization condition for the Fourier integral operators Ir m (X,Y;L )I_\rho ^\mu (X,Y;\it\Lambda ) leads to a parametrized parabolic Monge-Ampère equation. For an analytic operator, the fibration by the kernels of the Hessian of phase function is shown to be analytic in a number of cases, by considering a more general continuation problem for the level sets of a holomorphic mapping. The results are applied to obtain Lp-continuity for translation invariant operators in \Bbb Rn{\Bbb R}^n with n £ 4n\leq 4 and for arbitrary \Bbb Rn{\Bbb R}^n with dpX×Y|L £ n+2d\pi _{X\times Y}|_\Lambda \leq n+2. 相似文献
2.
We define a generalized Li coefficient for the L-functions attached to the Rankin–Selberg convolution of two cuspidal unitary automorphic representations π and π
′ of
GLm(\mathbbAF)GL_{m}(\mathbb{A}_{F})
and
GLm¢(\mathbbAF)GL_{m^{\prime }}(\mathbb{A}_{F})
. Using the explicit formula, we obtain an arithmetic representation of the n th Li coefficient
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
attached to
L(s,pf×[(p)\tilde]f¢)L(s,\pi _{f}\times \widetilde{\pi}_{f}^{\prime })
. Then, we deduce a full asymptotic expansion of the archimedean contribution to
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
and investigate the contribution of the finite (non-archimedean) term. Under the generalized Riemann hypothesis (GRH) on non-trivial
zeros of
L(s,pf×[(p)\tilde]f¢)L(s,\pi _{f}\times \widetilde{\pi}_{f}^{\prime })
, the nth Li coefficient
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
is evaluated in a different way and it is shown that GRH implies the bound towards a generalized Ramanujan conjecture for
the archimedean Langlands parameters μ
π
(v,j) of π. Namely, we prove that under GRH for
L(s,pf×[(p)\tilde]f)L(s,\pi _{f}\times \widetilde{\pi}_{f})
one has
|Remp(v,j)| £ \frac14|\mathop {\mathrm {Re}}\mu_{\pi}(v,j)|\leq \frac{1}{4}
for all archimedean places v at which π is unramified and all j=1,…,m. 相似文献
3.
We study the problem of strong uniqueness in Lp for the Dirichlet operator perturbed by a singular complex-valued potential. First we construct the generator -Hp of a C0-semigroup in Lp, with Hp extending the restriction of the perturbed Dirichlet operator to the set of smooth functions. The corresponding sesquilinear form in L2 is not assumed to be sectorial. Then we reveal sufficient conditions on the logarithmic derivative # of the measure rdx \rho dx and the potential q which ensure that -Hp is the only extension of D+b·?-q \upharpoonrightC0¥ \Delta +\beta \cdot \nabla -q \upharpoonright_{C_0^{\infty}} which generates a C0-semigroup on Lp. The method of a priori estimates of solutions to corresponding differential equations is employed. 相似文献
4.
Lasha Ephremidze Gigla Janashia Edem Lagvilava 《Journal of Fourier Analysis and Applications》2011,17(5):976-990
It is proved that if positive definite matrix functions (i.e. matrix spectral densities) S
n
, n=1,2,… , are convergent in the L
1-norm, ||Sn-S||L1? 0\|S_{n}-S\|_{L_{1}}\to 0, and ò02plogdetSn(eiq) dq?ò02plogdetS(eiq) dq\int_{0}^{2\pi}\log \mathop{\mathrm{det}}S_{n}(e^{i\theta})\,d\theta\to\int_{0}^{2\pi}\log \mathop{\mathrm{det}}S(e^{i\theta})\,d\theta, then the corresponding (canonical) spectral factors are convergent in L
2, ||S+n-S+||L2? 0\|S^{+}_{n}-S^{+}\|_{L_{2}}\to 0. The formulated logarithmic condition is easily seen to be necessary for the latter convergence to take place. 相似文献
5.
The generalized maximal operator M in martingale spaces is considered. For 1 < p ≤ q < ∞, the authors give a necessary and sufficient condition on the pair ([^(m)]\hat \mu , v) for M to be a bounded operator from martingale space L
p
(v) into L
q
([^(m)]\hat \mu ) or weak-L
q
([^(m)]\hat \mu ), where [^(m)]\hat \mu is a measure on Ω × ℕ and v a weight on Ω. Moreover, the similar inequalities for usual maximal operator are discussed. 相似文献
6.
Qingliu Yao 《Acta Appl Math》2010,110(2):871-883
This paper studies the existence of a positive solution to the second-order periodic boundary value problem
u¢¢(t)+l(t)u(t)=f(t,u(t)), 0 < t < 2p, u(0)=u(2p), u¢(0)=u¢(2p),u^{\prime \prime }(t)+\lambda (t)u(t)=f\bigl(t,u(t)\bigr),\quad 0 7.
Viorel Catană 《Integral Equations and Operator Theory》2010,66(1):41-52
We give a formula for the one-parameter strongly continuous semigroups ${e^{-tL^{\lambda}}}
8.
J.-C. Puchta 《Archiv der Mathematik》2000,74(4):266-268
Let h[-(p)h^-(p) be the relative class number of the p-th cyclotomic field. We show that logh-(p) = [(p+3)/4] logp - [(p)/2] log2p+ log(1-b) + O(log22 p)\log h^-(p) = {{p+3} \over {4}} \log p - {{p} \over {2}} \log 2\pi + \log (1-\beta ) + O(\log _2^2 p), where b\beta denotes a Siegel zero, if such a zero exists and p o -1 mod 4p\equiv -1\pmod {4}. Otherwise this term does not appear. 相似文献
9.
We consider the Hill operator
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