Topic
Densely defined operator
About: Densely defined operator is a research topic. Over the lifetime, 103 publications have been published within this topic receiving 1049 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, the Fourier transform of a convolutional operator on an abelian group G is defined as a closed densely defined operator which is equivalent to a multiplication in L2(G) by a measurable function on G.
Abstract: acter group G of G given by F(X) =f Gx(a)f(a)da; when f is in L1(G)nL2(G), T: f->F is an isometric map into L2(G) which can be extended to an isometry of L2(G) with L2(G). Moreover the operation Lf of convolution byf in L2(G) is unitarily equivalent via T to multiplication, Mp by F in L2(G). In fact MF= TLfT-1. If G is abelian, any closed densely defined operator in L2(G) which commutes with the group translations is equivalent via T to a multiplication in L2(G) by a measurable function on G, (Segal [4]). In particular if f is measurable on the abelian group G and Lf is closed and densely defined with TLfT-1 = M it is natural to call F the Fourier transform of f. Since F and MP are essentially equivalent it makes sense to define the Fourier
167 citations
TL;DR: A composition of weighted pseudo almost automorphic in a general Banach space is established and existence results are obtained by means of Banach contraction mapping to study the existence and uniqueness of a weighted pseudoAlmost Automorphic solution to fractional diffusion wave equation with Dirichlet conditions.
46 citations
TL;DR: In this article, the authors give conditions for invariance of regular operators under graph perturbations: when is the perturbation of a regular operator again a R.O?
42 citations
TL;DR: In this article, the existence and controllability of mild and extremal mild solutions for first-order semilinear densely defined impulsive functional differential inclusions in separable Banach spaces with local and nonlocal conditions were proved.
Abstract: In this paper we prove the existence and the controllability of mild and extremal mild solutions for first-order semilinear densely defined impulsive functional differential inclusions in separable Banach spaces with local and nonlocal conditions.
38 citations
TL;DR: The spectral mapping theorems and perturbation theorem for Browder's essential spectrum of T, ess (T) were derived in this paper for a closed, densely defined linear operator T and a bounded linear operator B which commutes with T.
Abstract: If T is a closed, densely defined linear operator in a Banach space, F. E. Browder has defined the essential spectrum of T, ess (T) [1]. We derive below spectral mapping theorems and perturbation theorems for Browder's essential spectrum. If T is a bounded linear operator and f is a function analytic on a neighborhood of the spectrum of T, we prove that f(ess (T)) = ess (f(T)). If T is a closed, densely defined linear operator with nonempty resolvent set and f is a polynomial, the same theorem holds. For a closed, densely defined linear operator T and a bounded linear operator B which commutes with T, we prove that ess (T+ B) ' ess (T) + ess (B) = { + v: e E ess (T), v E ess (B)}. By making additional assumptions, we obtain an analogous theorem for B unbounded. Introduction. Let T be a closed, densely defined linear operator on a Banach space X. F. E. Browder [1] defined the essential spectrum of T, ess (T), to be the set of A E a(T), the spectrum of T, such that at least one of the following conditions holds: (1) R(A-T), the range of A-T, is not closed; (2) A is a limit point of a(T); (3) Ur >o N[(A T)T] is infinite dimensional, where N(A) denotes the null space of a linear operator A. Browder proved that Ao 0 ess (T) if and only if (A -T)is defined for 0 < IA AO < 8 and the Laurent expansion of (A T) 1 around Ao has only a finite number of nonzero coefficients with negative indices. Recall that a closed, densely defined operator T is called a Fredholm operator if and only if dim N(T)
37 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 6 |
| 2020 | 6 |
| 2019 | 1 |
| 2018 | 7 |
| 2017 | 3 |
| 2016 | 3 |