0000000001325698
AUTHOR
Tschinke Francesco
showing 8 related works from this author
MR3730338 Reviewed de Jeu, Marcel(NL-LEID-MI); Tomiyama, Jun(J-TOKYM) The closure of ideals of ℓ1(Σ) in its enveloping C∗-algebra. (English summary) …
2018
Given a compact Hausdorff space X and a homeomorphism σ on X, denote by Σ=(X,σ) a topological dynamical system. Then the associated Banach ∗-algebra ℓ1(Σ) is defined as ℓ1(Σ)={a:Z→C(X), ∥a∥:=∑n∈Z∥a(n)∥<∞} with a crossed product–type product (aa′)(n)=∑k∈Za(k)⋅αk(a′(n−k)) and involution a∗(n)=αn(a(−n))¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯, where C(X) denote the space of complex-valued continuous functions on X, and α(f):=f∘σ−1 for f∈C(X). If C∗(Σ) is the enveloping C∗-algebra of ℓ1(Σ), considering a primitive ideal I of ℓ1(Σ), the authors show that there exists a ∗-representation π of ℓ1(Σ) on Hilbert space such that the kernel is I, and that the closure in C∗(Σ) of an ideal of ℓ1(Σ) is an ideal of C∗(Σ).
MR3785684 Reviewed Liu, Ai Fang(PRC-NAA); Li, Peng Tong(PRC-NAA) K-fusion frames and the corresponding generators for unitary systems. (English summa…
2018
Given an operator K∈B(H), in this paper the authors introduce K-fusion frames as a generalization of fusion frames, defined as a sequence {Wi} of closed subspaces of the Hilbert space H. For K=1, this becomes a fusion frame. They prove some properties of K-fusion frames, based on considering the operator K and the frame operators. In the last section, for a unitary system U, the authors define a K-fusion frame generator in a way similar to the frame vectors for unitary systems. Some properties and characterization theorems are derived for operators in the generalized local commutant of U.
MR3631681 Reviewed Nigsch, E. A.(A-WIENM) On a nonlinear Peetre's theorem in full Colombeau algebras. (English summary) Comment. Math. Univ. Carolin.…
2017
Colombeau algebras are defined as quotients of spaces containing the representatives of generalized functions given by smooth mappings: R:C∞(Ω,D(Ω))→C∞(Ω), where Ω is an open subset of Rn. In this paper the notion of locality defined by the author for a representative R of a nonlinear generalized function is characterized in such a way that the representative depends only on its ∞-jet. Finally, the author examines the possibility of defining a notion of order for the mapping R.
MR3714763 Reviewed Bargetz, C.(A-INSB); Nigsch, E. A.(A-WIEN-WPI); Ortner, N.(A-INSB) Convolvability and regularization of distributions. (English su…
2018
Referring to the theory of vector-valued distributions due to L. Schwartz, the authors, starting from a formulation due to Hirata and Shiraishi, carry out a study about generalizations of the convolvability and regularization of distributions, without test functions but by means of kernels. Further topological features, such as boundedness and relative compactness of subsets of distributions, are exhibited in light of previous results.
MR3667002 Reviewed Vogt, Dietmar(D-BUW) Hadamard operators on D′(Ω). (English summary) Math. Nachr. 290 (2017), no. 8-9, 1374–1380. 46F10 (46F12 47B3…
2017
In this paper, the Hadamard operators, i.e. a particular class of continuous linear operators on D′(Ω) whose set of eigenvectors is the class of monomials, are considered on an open set Ω⊂Rd. Specifically, Hadamard operators L are characterized by the multiplicative convolution, that is, there exists a distribution T such that L(S)=S⋆T, where the multiplicative convolution ⋆ is defined by (S⋆T)ϕ=Sy(Txϕ(xy)). To obtain this characterization, the author defines a particular extension to D(Ω˜), where Ω˜:=⋃a∈RdaΩ, of the transpose of Hadamard operators. This result is a generalization of a previous work of the author where only the case Ω=Rd was considered.
MR3428804 Reviewed Benci, Vieri(I-PISA); Luperi Baglini, Lorenzo(A-WIENM) Generalized functions beyond distributions. (English, Arabic summary) Arab.…
2016
Generalized functions are here intended to mean a particular class V˜(Ω) of ultrafunctions, i.e. functions defined on a non-Archimedean field that extends a class V(Ω) of L2(Ω)-integrable continuous functions. The particular class of ultrafunctions is selected by some desiderata to obtain the properties sufficient for applications to PDE. One of these is to maintain the locality property of a local operator defined on V(Ω) when it is extended to V˜(Ω). This fact is related to the possibility of defining a sort of orthogonality between "Delta ultrafunctions''. The results are applied to the definition of the derivative operator, the definite integral and to associate an ultrafunction to ever…
MR3586679 Reviewed Maksimović, Snježana(BS-BALUEL); Mincheva-Kamińska, Svetlana(PL-RZSZM); Pilipović, Stevan(SE-NOVIS-NDM); Sokoloski, Petar(MK-SKOPN…
2017
The purpose of the paper is to investigate ultradistributions of both Beurling and Roumieu (briefly, B and R) types with the help of a sequential approach, considering certain equivalence classes of fundamental sequences of smooth functions defined by ultradifferential operators. More precisely, the authors define as s-ultradistributions the equivalence classes U(t) and U{t} of B and R types respectively on test functions belonging respectively to D′(t)(Ω) and D′{t}(Ω) on the open set Ω⊂Rn, and T(t), T{t}, T~(t) and T~{t} of (tempered) t- and t~-distributions, and study their properties. Finally, the authors prove the existence of topological isomorphism between the classes T(t), T{t}, T~(t…
MR3535311 Reviewed Inoue, H.(J-KYUSGM); Takakura, M.(J-FUE-AM) Regular biorthogonal pairs and pseudo-bosonic operators. (English summary) J. Math. Ph…
2017
Given a pair of operators a and b acting on a Hilbert space H, such that [a,b]=1, the authors give a method to construct a regular bi-orthogonal pair of sequences in H. They study the relationship between the conditions on a,b,a†,b† and the operators Ae,Be,A†e,B†e, considered by one of the authors in a previous paper, in the set-up of a general theory of bi-orthogonal pair sequences. Then they give a method to construct operators A and B with the so-called D-pseudo bosons conditions, i.e. the commutation rule and some assumptions, on a dense subspace D of H, considered in the literature. Finally, some physical examples are given.