• Corpus ID: 119129876

# On the generation of groups of bounded linear operators on Fr\'{e}chet spaces

@article{Costa2017OnTG,
title={On the generation of groups of bounded linear operators on Fr\'\{e\}chet spaces},
author={'Eder R'itis Aragao Costa and Alexxandro Silva},
journal={arXiv: Analysis of PDEs},
year={2017}
}
• Published 3 March 2017
• Mathematics
• arXiv: Analysis of PDEs
In this paper we present a general method for generation of uniformly continuous groups on abstract Frechet spaces (without appealing to spectral theory) and apply it to a such space of distributions, namely ${\mathscr F}L^{2}_{loc}(\mathbb{R}^{n})$, so that the linear evolution problem \begin{equation*} \left\{\begin{array}{l} u_{t} = a(D)u, t \in \mathbb{R} \\ u(0) = u_0 \end{array} \right. \end{equation*}always has a unique solution in such a space, for every pseudodifferential operator $a(D… 1 Citations In this paper we prove versions, in Frechet spaces, of the classical theorems related to exponential dichotomy for a sequence of continuous linear operators on Banach spaces. To be more specific, ## References SHOWING 1-10 OF 28 REFERENCES In this paper we prove versions, in Frechet spaces, of the classical theorems related to exponential dichotomy for a sequence of continuous linear operators on Banach spaces. To be more specific, We consider locally equi-continuous strongly continuous semigroups on locally convex spaces $$(X,\tau )$$(X,τ) that are also equipped with a ‘suitable’ auxiliary norm. We introduce the set$\$\mathcal
ing the above, for a (not necessarily countable) family . . . φ2 // B1 φ1 // Bo of Banach spaces with continuous linear transition maps as indicated, not recessarily requiring the continuous linear
This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different
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The main purpose is to generalize a theorem of Arendt about uniqueness of C0-semigroups from Banach space setting to general locally convex vector spaces. More precisely, we show that cores are the
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• 2011
1. Some Classical Theorems.- 1.1. The Riesz-Thorin Theorem.- 1.2. Applications of the Riesz-Thorin Theorem.- 1.3. The Marcinkiewicz Theorem.- 1.4. An Application of the Marcinkiewicz Theorem.- 1.5.
A vector space over a field K (R or C) is a set X with operations vector addition and scalar multiplication satisfy properties in section 3.1. [1] An inner product space is a vector space X with