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Sat, 04 Mar 2000 00:00:00 +0200Sat, 04 Mar 2000 00:00:00 +0200New Integral Representations for the Square of the Riemann Zeta-function
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/817
Andreas Guthmannpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/817Mon, 03 Apr 2000 00:00:00 +0200On the efficient discretization of integral equations of the third kind
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/825
We propose a new discretization scheme for solving ill-posed integral equations of the third kind. Combining this scheme with Morozov's discrepancy principle for Landweber iteration we show that for some classes of equations in such method a number of arithmetic operations of smaller order than in collocation method is required to appoximately solve an equation with the same accuracy.Sergei V. Pereverzev; Eberhard Schock; Sergei G. Solodkypreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/825Mon, 03 Apr 2000 00:00:00 +0200Asymptotic Expansions for Dirichlet Series Associated to Cusp Forms
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/826
We prove an asymptotic expansion of Riemann-Siegel type for Dirichlet series associated to cusp forms. Its derivation starts from a new integral formula for the Dirichlet series and uses sharp asymptotic expansions for partial sums of the Fourier series of the cusp form.Andreas Guthmannpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/826Mon, 03 Apr 2000 00:00:00 +0200Pointwise decay of solutions and of higher derivatives to Navier-Stokes equations
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/832
In this paper we study the space-time asymptotic behavior of the solutions and derivatives to th incompressible Navier-Stokes equations. Using moment estimates we obtain that strong solutions to the Navier-Stokes equations which decay in \(L^2\) at the rate of \(||u(t)||_2 \leq C(t+1)^{-\mu}\) will have the following pointwise space-time decay \[|D^{\alpha}u(x,t)| \leq C_{k,m} \frac{1}{(t+1)^{ \rho_o}(1+|x|^2)^{k/2}} \]
where \( \rho_o = (1-2k/n)( m/2 + \mu) + 3/4(1-2k/n)\), and \(|a |= m\). The dimension n is \(2 \leq n \leq 5\) and \(0\leq k\leq n\) and \(\mu \geq n/4\)Cherif Amrouche; Vivette Girault; Maria Elena Schonbek; Thomas P. Schonbekpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/832Mon, 03 Apr 2000 00:00:00 +0200Pathwise Kallianpur-Robbins laws for Brownian motion in the plane
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/840
The Kallianpur-Robbins law describes the long term asymptotic behaviour of the distribution of the occupation measure of a Brownian motion in the plane. In this paper we show that this behaviour can be seen at every typical Brownian path by choosing either a random time or a random scale according to the logarithmic laws of order three. We also prove a ratio ergodic theorem for small scales outside an exceptional set of vanishing logarithmic density of order three.Peter MÃ¶rterspreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/840Fri, 28 Jan 2000 00:00:00 +0100