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pro vyhledávání: '"47D06"'
Existence and explicit formula for a semigroup related to some network problems with unbounded edges
Autor:
Błoch, Adam
In this paper we consider an initial-boundary value problem related to some network dynamics where the underlying graph has unbounded edges. We show that there exists a C0-semigroup for this problem using a general result from the literature. We also
Externí odkaz:
http://arxiv.org/abs/2409.11903
Autor:
Oliveira, Geronimo, Viana, Arlúcio
In this work, we study the heat equation with Grushin's operator. We present an expression for its heat kernel and get regularity properties and decay on $L^p$ spaces for both heat Kernel and semigroup associated to Grushin's operator. Next, we use t
Externí odkaz:
http://arxiv.org/abs/2409.06578
Autor:
Kruse, Karsten, Schwenninger, Felix L.
We study maximal regularity with respect to continuous functions for strongly continuous semigroups on locally convex spaces as well as its relation to the notion of admissible operators. This extends several results for classical strongly continuous
Externí odkaz:
http://arxiv.org/abs/2408.11437
Autor:
Trapasso, S. Ivan
We perform a phase space analysis of evolution equations associated with the Weyl quantization $q^{\mathrm{w}}$ of a complex quadratic form $q$ on $\mathbb{R}^{2d}$ with non-positive real part. In particular, we obtain pointwise bounds for the matrix
Externí odkaz:
http://arxiv.org/abs/2408.11130
We consider a bounded representation $T$ of a commutative semigroup $S$ on a Banach space and analyse the relation between three concepts: (i) properties of the unitary spectrum of $T$, which is defined in terms of semigroup characters on $S$; (ii) u
Externí odkaz:
http://arxiv.org/abs/2408.08961
In this paper we consider BIBO stability of infinite-dimensional linear state-space systems and the related notion of $L^1$-to-$L^1$ input-output stability (abbreviated LILO). We show that in the case of finite-dimensional input and output spaces, bo
Externí odkaz:
http://arxiv.org/abs/2408.06313
Autor:
Arora, Sahiba, Schwenninger, Felix L.
We extend classical duality results by Weiss on admissible operators to settings where the dual semigroup lacks strong continuity. This is possible using the sun-dual framework, which is not immediate from the duality of the input and output maps. Th
Externí odkaz:
http://arxiv.org/abs/2408.02150
We obtain polynomial decay rates for $C_{0}$-semigroups, assuming that the resolvent grows polynomially at infinity in the complex right half-plane. Our results do not require the semigroup to be uniformly bounded, and for unbounded semigroups we imp
Externí odkaz:
http://arxiv.org/abs/2407.09323
The method of Feynman-Kac perturbation of quantum stochastic processes has a long pedigree, with the theory usually developed within the framework of processes on von Neumann algebras. In this work, the theory of operator spaces is exploited to enabl
Externí odkaz:
http://arxiv.org/abs/2407.06732
Autor:
Bernád, J. Z., Frigyik, A. B.
Often, when we consider the time evolution of a system, we resort to approximation: Instead of calculating the exact orbit, we divide the time interval in question into uniform segments. Chernoff's results in this direction provide us with a general
Externí odkaz:
http://arxiv.org/abs/2407.04357