Representation of complex powers of C-sectorial operators

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Chuang Chen ◽  
Marko Kostić ◽  
Miao Li
Keyword(s):  
Linear Operators ◽  
Locally Convex Spaces ◽  
Sectorial Operators ◽  
Complex Powers ◽  
Locally Convex ◽  
Resolvent Families ◽  
Closed Linear Operators ◽  
Convex Spaces

AbstractThe paper is devoted to the study of representation of complex powers of closed linear operators whose negatives generate equicontinuous (g α, C)-regularized resolvent families (0 < α ≤ 2) on sequentially complete locally convex spaces. Several interesting formulas regarding powers and their domains are proved.

scholarly journals Systems of abstract time-fractional equations

2014 ◽  
Vol 95 (109) ◽  
pp. 119-132 ◽  
Author(s):  
Marko Kostic
Keyword(s):  
Semigroups Of Operators ◽  
Locally Convex Spaces ◽  
Fractional Equations ◽  
Locally Convex ◽  
Resolvent Families ◽  
Convex Spaces

We analyze systems of abstract time-fractional equations in certain classes of sequentially complete locally convex spaces. We also consider arbitrary matrices of operators as generators of fractional regularized resolvent families, improving in such a way the results known for semigroups of operators.

scholarly journals On numerical ranges of operators on locally convex spaces

1975 ◽  
Vol 20 (4) ◽  
pp. 468-482 ◽  
Author(s):  
J. R. Giles ◽  
G. Joseph ◽  
D. O. Koehler ◽  
B. Sims
Keyword(s):  
Numerical Range ◽  
Linear Operators ◽  
Locally Convex Spaces ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Range Theory ◽  
Locally Convex ◽  
Convex Spaces

Numerical range theory for linear operators on normed linear spaces and for elements of normed algebras is now firmly established and the main results of this study are conveniently presented by Bonsall and Duncan in (1971) and (1973). An extension of the spatial numerical range for a class of operators on locally convex spaces was outlined by Moore in (1969) and (1969a), and an extension of the algebra numerical range for elements of locally m-convex algebras was presented by Giles and Koehler (1973). It is our aim in this paper to contribute further to Moore's work by extending the concept of spatial numerical range to a wider class of operators on locally convex spaces.

scholarly journals Degenerate abstract Volterra equations in locally convex spaces

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 597-619
Author(s):  
Marko Kostic
Keyword(s):  
Resolvent Operator ◽  
Final Section ◽  
Differential Operators ◽  
Volterra Equations ◽  
Locally Convex Spaces ◽  
Efficient Tool ◽  
Scalar Type ◽  
Locally Convex ◽  
Resolvent Families ◽  
Convex Spaces

In the paper under review, we analyze various types of degenerate abstract Volterra integrodifferential equations in sequentially complete locally convex spaces. From the theory of non-degenerate equations, it is well known that the class of (a,k)-regularized C-resolvent families provides an efficient tool for dealing with abstract Volterra integro-differential equations of scalar type. Following the approach of T.-J. Xiao and J. Liang [41]-[43], we introduce the class of degenerate exponentially equicontinuous (a,k)- regularized C-resolvent families and discuss its basic structural properties. In the final section of paper, we will look at generation of degenerate fractional resolvent operator families associated with abstract differential operators.

Linear Chaos on Fréchet Spaces

2003 ◽  
Vol 13 (07) ◽  
pp. 1649-1655 ◽  
Author(s):  
J. Bonet ◽  
F. Martínez-Giménez ◽  
A. Peris
Keyword(s):  
Linear Operators ◽  
Locally Convex Spaces ◽  
Fréchet Spaces ◽  
Continuous Linear ◽  
Locally Convex ◽  
Continuous Linear Operators ◽  
Convex Spaces

This is a survey on recent results about hypercyclicity and chaos of continuous linear operators between complete metrizable locally convex spaces. The emphasis is put on certain contributions from the authors, and related theorems.

scholarly journals On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-41
Author(s):  
Marko Kostić ◽  
Cheng-Gang Li ◽  
Miao Li
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Convex Space ◽  
Existence And Uniqueness ◽  
Locally Convex Space ◽  
Linear Operators ◽  
Locally Convex Spaces ◽  
Fractional Equations ◽  
Locally Convex ◽  
Closed Linear Operators

This paper is devoted to the study of abstract time-fractional equations of the following form:Dtαnu(t)+∑i=1n−1AiDtαiu(t)=ADtαu(t)+f(t),t>0,u(k)(0)=uk,k=0,...,⌈αn⌉−1, wheren∈ℕ∖{1},AandA1,...,An−1are closed linear operators on a sequentially complete locally convex spaceE,0≤α1<⋯<αn,0≤α<αn,f(t)is anE-valued function, andDtαdenotes the Caputo fractional derivative of orderα(Bazhlekova (2001)). We introduce and systematically analyze various classes ofk-regularized (C1,C2)-existence and uniqueness (propagation) families, continuing in such a way the researches raised in (de Laubenfels (1999, 1991), Kostić (Preprint), and Xiao and Liang (2003, 2002). The obtained results are illustrated with several examples.

Some special operators and new classes of locally convex spaces

1972 ◽  
Vol 71 (3) ◽  
pp. 475-489 ◽  
Author(s):  
Ajit Kaur Chilana
Keyword(s):  
Hausdorff Space ◽  
Linear Operators ◽  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Locally Convex ◽  
Continuous Linear Operators ◽  
Convex Spaces ◽  
Special Classes

AbstractWe consider some special operators on a locally convex Hausdorff space to itself, which have neat spectral theories and prove some perturbation results. This leads us to define and study a few special classes of locally convex spaces in which various subsets of the algebra of continuous linear operators either coincide or are closely related with each other. These are then compared to the classes of barrelled, infrabarrelled and DF-spaces and examples are given to distinguish them from one another.

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