Search results for "asymptotic expansion"
showing 10 items of 38 documents
Zero viscosity limit of the Oseen equations in a channel
2001
Oseen equations in the channel are considered. We give an explicit solution formula in terms of the inverse heat operators and of projection operators. This solution formula is used for the analysis of the behavior of the Oseen equations in the zero viscosity limit. We prove that the solution of Oseen equations converges in W1,2 to the solution of the linearized Euler equations outside the boundary layer and to the solution of the linearized Prandtl equations inside the boundary layer. © 2001 Society for Industrial and Applied Mathematics.
Complex powers of elliptic pseudodifferential operators
1986
The aim of this paper is the construction of complex powers of elliptic pseudodifferential operators and the study of the analytic properties of the corresponding kernels kS (x,y). For x=y, the case of principal interest, the domain of holomorphy and the singularities of kS (x,x) are shown to depend on the asymptotic expansion of the symbol. For classical symbols, kS (x,x) is known to be meromorphic on ℂ with simple poles in a set of equidistant points on the real axis. In the more general cases considered here, the singularities may be distributed over a half plane and kS (x,x) can not always be extended to337-2. An example is given where kS (x,x) has a vertical line as natural boundary.
A form factor approach to the asymptotic behavior of correlation functions in critical models
2011
We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states to one over the particle/hole excitations lying on the Fermi surface in the thermodynamic limit. We compute these sums, over the so-called critical form factors, exactly. Thus we obtain the leading large distance behavior of each oscillating harmonic of the correlation function asymptotic expansion, including the corresponding amplitudes. Our method is applicable to a wide variety of integrable models and yields precisely the results stemming from the Lutt…
Application of the star-product method to the angular momentum quantization
1992
We define a *-product on ℝ3 and solve the polarization equation f*C=0 where C is the Casimir of the coadjoint representation of SO(3). We compute the action of SO(3) on the space of solutions. We then examine the case of non-zero eigenvalues of C, in order to find finite-dimensional representations of SO(3). Finally, we compute \(\sqrt C *\sqrt C \) as an asymptotic series of C. This gives an explanation of the use of the star square root of C in a paper by Bayen et al. instead of its natural square root.
Method of analytic continuation by duality in QCD: Beyond QCD sum rules
1986
We present the method of analytic continuation by duality which allows the approximate continuation of QCD amplitudes to small values of the momentum variables where direct perturbative calculations are not possible. This allows a substantial extension of the domain of applications of hadronic QCD phenomenology. The method is illustrated by a simple example which shows its essential features.
Solutions of nonlinear PDEs in the sense of averages
2012
Abstract We characterize p-harmonic functions including p = 1 and p = ∞ by using mean value properties extending classical results of Privaloff from the linear case p = 2 to all pʼs. We describe a class of random tug-of-war games whose value functions approach p-harmonic functions as the step goes to zero for the full range 1 p ∞ .
Unfolding of saddle-nodes and their Dulac time
2016
Altres ajuts: UNAB10-4E-378, co-funded by ERDF "A way to build Europe" and by the French ANR-11-BS01-0009 STAAVF. In this paper we study unfoldings of saddle-nodes and their Dulac time. By unfolding a saddle-node, saddles and nodes appear. In the first result (Theorem A) we give a uniform asymptotic expansion of the trajectories arriving at the node. Uniformity is with respect to all parameters including the unfolding parameter bringing the node to a saddle-node and a parameter belonging to a space of functions. In the second part, we apply this first result for proving a regularity result (Theorem B) on the Dulac time (time of Dulac map) of an unfolding of a saddle-node. This result is a b…
Asymptotic stability of solutions to Volterra-renewal integral equations with space maps
2012
Abstract In this paper we consider linear Volterra-renewal integral equations (VIEs) whose solutions depend on a space variable, via a map transformation. We investigate the asymptotic properties of the solutions, and study the asymptotic stability of a numerical method based on direct quadrature in time and interpolation in space. We show its properties through test examples.
On lacunary Toeplitz determinants
2014
By using Riemann--Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants $\det_N\big[ c_{\ell_a-m_b}[f] \big]$ generated by holomorhpic symbols, where $\ell_a=a$ (resp. $m_b=b$) except for a finite subset of indices $a=h_1,\dots, h_n$ (resp. $b=t_1,\dots, t_r$). In addition to the usual Szeg\"{o} asymptotics, our answer involves a determinant of size $n+r$.
A note on Einstein gravity on AdS(3) and boundary conformal field theory
1998
We find a simple relation between the first subleading terms in the asymptotic expansion of the metric field in AdS$_3$, obeying the Brown-Henneaux boundary conditions, and the stress tensor of the underlying Liouville theory on the boundary. We can also provide an more explicit relation between the bulk metric and the boundary conformal field theory when it is described in terms of a free field with a background charge.