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Spectral theory of SG pseudo-differential operators on L p ( )

Aparajita Dasgupta, M. W. Wong (2008)

Studia Mathematica

To every elliptic SG pseudo-differential operator with positive orders, we associate the minimal and maximal operators on L p ( ) , 1 < p < ∞, and prove that they are equal. The domain of the minimal ( = maximal) operator is explicitly computed in terms of a Sobolev space. We prove that an elliptic SG pseudo-differential operator is Fredholm. The essential spectra of elliptic SG pseudo-differential operators with positive orders and bounded SG pseudo-differential operators with orders 0,0 are computed....

Spectral theta series of operators with periodic bicharacteristic flow

Jens Marklof (2007)

Annales de l’institut Fourier

The theta series ϑ ( z ) = exp ( 2 π i n 2 z ) is a classical example of a modular form. In this article we argue that the trace ϑ P ( z ) = Tr exp ( 2 π i P 2 z ) , where P is a self-adjoint elliptic pseudo-differential operator of order 1 with periodic bicharacteristic flow, may be viewed as a natural generalization. In particular, we establish approximate functional relations under the action of the modular group. This allows a detailed analysis of the asymptotics of ϑ P ( z ) near the real axis, and the proof of logarithm laws and limit theorems for its value...

Stability of hydrodynamic model for semiconductor

Massimiliano Daniele Rosini (2005)

Archivum Mathematicum

In this paper we study the stability of transonic strong shock solutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construction of a pseudo-local symmetrizer and on the paradifferential calculus with parameters, which combines the work of Bony-Meyer and the introduction of a large parameter.

Stokes equations in asymptotically flat layers

Helmut Abels (2005)

Banach Center Publications

We study the generalized Stokes resolvent equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer Ω = n - 1 × ( - 1 , 1 ) . Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. We discuss the results on unique solvability of the generalized Stokes resolvent equations as well as the existence of a bounded H -calculus for the associated Stokes operator and some...

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