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Asymptotics of sums of subcoercive operators

Nick Dungey, A. ter Elst, Derek Robinson (1999)

Colloquium Mathematicae

We examine the asymptotic, or large-time, behaviour of the semigroup kernel associated with a finite sum of homogeneous subcoercive operators acting on a connected Lie group of polynomial growth. If the group is nilpotent we prove that the kernel is bounded by a convolution of two Gaussians whose orders correspond to the highest and lowest orders of the homogeneous subcoercive components of the generator. Moreover we establish precise asymptotic estimates on the difference of the kernel and the...

Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one.

Alexander V. Sobolev (2006)

Revista Matemática Iberoamericana

We consider a periodic pseudo-differential operator on the real line, which is a lower-order perturbation of an elliptic operator with a homogeneous symbol and constant coefficients. It is proved that the density of states of such an operator admits a complete asymptotic expansion at large energies. A few first terms of this expansion are found in a closed form.

Attractors of Strongly Dissipative Systems

A. G. Ramm (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

A class of infinite-dimensional dissipative dynamical systems is defined for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see, e.g., MR0601947...

Automatic continuity of biseparating maps

Jesús Araujo, Krzysztof Jarosz (2003)

Studia Mathematica

We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when this is not true.

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