scholarly journals Optimal Randomized Multilevel Algorithms for Infinite-Dimensional Integration on Function Spaces with ANOVA-Type Decomposition

2014 ◽  
Vol 52 (3) ◽  
pp. 1128-1155 ◽  
Author(s):  
Jan Baldeaux ◽  
Michael Gnewuch
Keyword(s):  
Function Spaces ◽  
Multilevel Algorithms ◽  
Infinite Dimensional ◽  
Type Decomposition

scholarly journals Topological Dual Systems for Spaces of Vector Measurep-Integrable Functions

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
P. Rueda ◽  
E. A. Sánchez Pérez
Keyword(s):  
Type Theorem ◽  
Classical Case ◽  
Function Spaces ◽  
Dual Systems ◽  
Banach Function Spaces ◽  
Infinite Dimensional ◽  
Local Compactness ◽  
Finite Dimensional ◽  
Integrable Functions ◽  
Vector Valued

We show a Dvoretzky-Rogers type theorem for the adapted version of theq-summing operators to the topology of the convergence of the vector valued integrals on Banach function spaces. In the pursuit of this objective we prove that the mere summability of the identity map does not guarantee that the space has to be finite dimensional, contrary to the classical case. Some local compactness assumptions on the unit balls are required. Our results open the door to new convergence theorems and tools regarding summability of series of integrable functions and approximation in function spaces, since we may find infinite dimensional spaces in which convergence of the integrals, our vector valued version of convergence in the weak topology, is equivalent to the convergence with respect to the norm. Examples and applications are also given.

scholarly journals Functional Representations for Fock Superalgebras

1998 ◽  
Vol 01 (02) ◽  
pp. 285-324 ◽  
Author(s):  
Joachim Kupsch ◽  
Oleg G. Smolyanov
Keyword(s):  
Reproducing Kernel ◽  
Fock Space ◽  
Function Spaces ◽  
Graded Algebras ◽  
Fock Representation ◽  
Infinite Dimensional ◽  
Gaussian Integration ◽  
Classical Function ◽  
Functional Representations ◽  
Wick Ordering

The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite-dimensional superspaces, and construct super-analogs of the classical function spaces with a reproducing kernel — including the Bargmann–Fock representation — and of the Wiener–Segal representation. The latter representation requires the investigation of Wick ordering on Z2-graded algebras. As application we derive a Mehler formula for the Ornstein–Uhlenbeck semigroup on the Fock space.

scholarly journals Homogeneous Triebel-Lizorkin Spaces on Stratified Lie Groups

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Guorong Hu
Keyword(s):  
Lie Groups ◽  
Singular Integral ◽  
Full Range ◽  
Integral Operators ◽  
Function Spaces ◽  
Singular Integral Operators ◽  
Basic Properties ◽  
Stratified Lie Groups ◽  
Type Decomposition

Homogeneous Triebel-Lizorkin spaces with full range of parameters are introduced on stratified Lie groups in terms of Littlewood-Paley-type decomposition. It is shown that the scale of these spaces is independent of the choice of Littlewood-Paley-type decomposition and the sub-Laplacian used for the construction of the decomposition. Some basic properties of these spaces are given. As the main result of this paper, boundedness of a class of singular integral operators on these function spaces is obtained.

scholarly journals The Bishop-Phelps-Bollobàs Property for Compact Operators

2018 ◽  
Vol 70 (1) ◽  
pp. 53-57 ◽  
Author(s):  
Sheldon Dantas ◽  
Domingo García ◽  
Manuel Maestre ◽  
Miguel Martín
Keyword(s):  
Hilbert Space ◽  
Topological Space ◽  
Banach Spaces ◽  
Positive Measure ◽  
Compact Operators ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Nikodym Property

AbstractWe study the Bishop-Phelps-Bollobàs property (BPBp) for compact operators. We present some abstract techniques that allow us to carry the BPBp for compact operators from sequence spaces to function spaces. As main applications, we prove the following results. Let X and Y be Banach spaces. If (c0, Y) has the BPBp for compact operators, then so do (C0(L), Y) for every locally compactHausdorò topological space L and (X, Y) whenever X* is isometrically isomorphic to . If X* has the Radon-Nikodým property and (X), Y) has the BPBp for compact operators, then so does (L1(μ, X), Y) for every positive measure μ; as a consequence, (L1(μ, X), Y) has the BPBp for compact operators when X and Y are finite-dimensional or Y is a Hilbert space and X = c0 or X = Lp(v) for any positive measure v and 1 < p < ∞. For , if (X, (Y)) has the BPBp for compact operators, then so does (X, Lp(μ, Y)) for every positive measure μ such that L1(μ) is infinite-dimensional. If (X, Y) has the BPBp for compact operators, then so do (X, L∞(μ, Y)) for every σ-finite positive measure μ and (X, C(K, Y)) for every compact Hausdorff topological space K.

HOLOMORPHIC SUPERPOSITION OPERATORS BETWEEN BANACH FUNCTION SPACES

2013 ◽  
Vol 96 (2) ◽  
pp. 186-197 ◽  
Author(s):  
CHRISTOPHER BOYD ◽  
PILAR RUEDA
Keyword(s):  
Large Class ◽  
Holomorphic Functions ◽  
Function Spaces ◽  
Weighted Spaces ◽  
Banach Function Spaces ◽  
Infinite Dimensional ◽  
Spaces Of Holomorphic Functions ◽  
Infinite Dimensional Holomorphy ◽  
Superposition Operators ◽  
Alpha Beta

AbstractWe prove that for a large class of Banach function spaces continuity and holomorphy of superposition operators are equivalent and that bounded superposition operators are continuous. We also use techniques from infinite dimensional holomorphy to establish the boundedness of certain superposition operators. Finally, we apply our results to the study of superposition operators on weighted spaces of holomorphic functions and the $F(p, \alpha , \beta )$ spaces of Zhao. Some independent properties on these spaces are also obtained.

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