Root Operators and “Evolution” Equations

Root Operators and “Evolution” Equations

Root-operator factorization à la Dirac provides an effective tool to deal with equations, which are not of evolution type, or are ruled by fractional differential operators, thus eventually yielding evolution-like equations although for a multicomponent vector. We will review the method along with its extension to root operators of degree higher than two. Also, we will show the results obtained...

Evolution Equations with Causal Operators

In this paper we present an existence result for causal functional evolution equations. The result is obtained under a condition with respect to the Hausdorff measure of noncompactness. An application with partial differential equations is given to illustrate our main result. Mathematics subject classification (2010): 34A07, 34A08.

Relatively Closed Operators and Linear Evolution Equations

In this paper it is shown how the vector-valued Laplace transform can be used to obtain existence and uniqueness results for exponentially bounded solutions of abstract linear evolution equations in Banach spaces. The method allows to consider problems for which the characteristic operator is, like many sums, products or limits of closed operators, not necessarily closed or closable.

Evolution Equations Governed by Elliptic Operators

Migrativity equations and Mayor's aggregation operators

There has been a growing interest in the study of the notion of $alpha$-migrativity and generalizations in recent years, and it has been investigated for families of certain operators such as t-norms, t-conorms, uninorms, nullnorms.This paper is mainly devoted to investigating the migrativity equations between semi-t-operators or semi-uninorms, and Mayor's aggregation operators. The results tha...