EXOTIC LAPLACIANS AND DERIVATIVES OF WHITE NOISE

2011 ◽  
Vol 14 (01) ◽  
pp. 1-14 ◽  
Author(s):  
LUIGI ACCARDI ◽  
UN CIG JI ◽  
KIMIAKI SAITÔ
Keyword(s):  
Linear Operator ◽  
White Noise ◽  
Continuous Linear Operator ◽  
Higher Order ◽  
Continuous Linear ◽  
White Noise Functionals ◽  
Derivatives Of

In this paper, we give a relationship between the exotic Laplacians and the Lévy Laplacians in terms of the higher-order derivatives of white noise by introducing a bijective and continuous linear operator acting on white noise functionals. Moreover, we study a relationship between exotic Laplacians, acting on higher-order singular functionals, each other in terms of the constructed operator.

scholarly journals Transforms on white noise functionals with their applications to Cauchy problems

1997 ◽  
Vol 147 ◽  
pp. 1-23 ◽  
Author(s):  
Dong Myung Chung ◽  
Un Cig Ji
Keyword(s):  
Cauchy Problem ◽  
White Noise ◽  
Existence And Uniqueness ◽  
Continuous Linear Operator ◽  
Characterization Theorem ◽  
Cauchy Problems ◽  
Continuous Linear ◽  
The Cauchy Problem ◽  
White Noise Functionals ◽  
Generalized Laplacian

AbstractA generalized Laplacian ΔG(K) is defined as a continuous linear operator acting on the space of test white noise functionals. Operator-parameter - and -transforms on white noise functionals are introduced and then prove a characterization theorem for and -transforms in terms of the coordinate differential operator and the coordinate multiplication. As an application, we investigate the existence and uniqueness of solution of the Cauchy problem for the heat equation associated with ΔG(K)

scholarly journals Semi-embeddings of Banach spaces which are hereditarily c0

1983 ◽  
Vol 26 (2) ◽  
pp. 163-167 ◽  
Author(s):  
L. Drewnowski
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Vector Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Continuous Linear Operator ◽  
Closed Unit Ball ◽  
Continuous Linear ◽  
Scattered Space ◽  
Complete Set

Following Lotz, Peck and Porta [9], a continuous linear operator from one Banach space into another is called a semi-embedding if it is one-to-one and maps the closed unit ball of the domain onto a closed (hence complete) set. (Below we shall allow the codomain to be an F-space, i.e., a complete metrisable topological vector space.) One of the main results established in [9] is that if X is a compact scattered space, then every semi-embedding of C(X) into another Banach space is an isomorphism ([9], Main Theorem, (a)⇒(b)).

scholarly journals A note on Dunford-Pettis operators

1987 ◽  
Vol 29 (2) ◽  
pp. 271-273 ◽  
Author(s):  
J. R. Holub
Keyword(s):  
Linear Operator ◽  
Positive Operator ◽  
Continuous Linear Operator ◽  
Positive Operators ◽  
Regular Operator ◽  
Continuous Linear

Talagrand has shown [4, p. 76] that there exists a continuous linear operator from L1[0, 1] to c0 which is not a Dunford-Pettis operator. In contrast to this result, Gretsky and Ostroy [2] have recently proved that every positive operator from L[0, 1] to c0 is a Dunford-Pettis operator, hence that every regular operator between these spaces (i.e. a difference of positive operators) is Dunford-Pettis.

Linearization of a Contractive Homeomorphism

1968 ◽  
Vol 20 ◽  
pp. 1387-1390
Author(s):  
Ludvik Janos
Keyword(s):  
Linear Operator ◽  
Topological Space ◽  
Vector Space ◽  
Topological Vector Space ◽  
Continuous Linear Operator ◽  
Continuous Linear ◽  
Topological Embedding

Let X be a topological space and ϕ: X ⟶ X a continuous self-mapping of X. We say that ϕ is linearized in L by Φ if there exists a topological embedding μ: X ⟶ L of the space X into the linear topological vector space L such that for all x ϵ X, μ (ϕ (x)) = Φ (μ (x)), where ϕ is a continuous linear operator on L.

Bounded continuous linear operator on cone normed space C'[a,b] to C[a,b]

2016 ◽  
Vol 5 ◽  
pp. 65-73
Author(s):  
Sunarsini ◽  
Sadjidon ◽  
Agus Nur Ahmad Syarifudin
Keyword(s):  
Linear Operator ◽  
Normed Space ◽  
Continuous Linear Operator ◽  
Continuous Linear

scholarly journals On the spectrum of ψ-contracting operators

2001 ◽  
Vol 14 (3) ◽  
pp. 303-308 ◽  
Author(s):  
Anwar A. Al-Nayef
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Continuous Linear Operator ◽  
Continuous Linear ◽  
Hausdorff Measure Of Noncompactness

The spectrum σ(A) of a continuous linear operator A:E→E defined on a Banach space E, which is contracting with respect to the Hausdorff measure of noncompactness, is investigated.

scholarly journals Sufficient conditions for a continuous linear operator to be weakly compact

1972 ◽  
Vol 7 (2) ◽  
pp. 183-190 ◽  
Author(s):  
Joe Howard ◽  
Kenneth Melendez
Keyword(s):  
Linear Operator ◽  
Sufficient Conditions ◽  
Continuous Linear Operator ◽  
Continuous Operator ◽  
Continuous Linear ◽  
Weakly Compact ◽  
Completely Continuous ◽  
Completely Continuous Operator ◽  
Locally Convex

A locally convex topological vector (LCTV) space E is said to have property V (Dieudonné property) if for every complete separated LCTV space F, every unconditionally converging (weakly completely continuous) operator T: E → F is wsakly compact. First, an investigation of the permanence of property V is given. The permanence of the Dieudonné is analogous. Relationships between property V and the Dieudonné property are then given.

scholarly journals ON A CLASS OF POLYA PROPERTY PRESERVING OPERATORS

2020 ◽  
Vol 27 (4) ◽  
pp. 301-313
Author(s):  
CHIU-CHENG CHANG
Keyword(s):  
Linear Operator ◽  
Integral Representation ◽  
Kernel Function ◽  
Sufficient Conditions ◽  
Continuous Linear Operator ◽  
Continuous Linear

In this paper, we show that every continuous linear operator from H(OmegawXOmegaz) to H (OmegawxOmegaxi) has an integral representation with a kernel function M(z, w, xi). We give two sufficient conditions on M(z,w,() to ensure that its corresponding operator preserves Polya property. We also prove that a continuous linear operator from H(fl,,, x ) to H(! x S2() either preserves the Polya property for all functions with that property or does not preserve the Polya property for any function.

scholarly journals THE EXOTIC (HIGHER ORDER LÉVY) LAPLACIANS GENERATE THE MARKOV PROCESSES GIVEN BY DISTRIBUTION DERIVATIVES OF WHITE NOISE

2013 ◽  
Vol 16 (03) ◽  
pp. 1350020 ◽  
Author(s):  
LUIGI ACCARDI ◽  
UN CIG JI ◽  
KIMIAKI SAITÔ
Keyword(s):  
White Noise ◽  
Higher Order ◽  
Technical Tool ◽  
Arithmetic Means ◽  
Infinite Dimensional ◽  
Second Derivatives ◽  
Lévy Laplacian ◽  
Order Arithmetic ◽  
Derivatives Of ◽  
Main Technical Tool

We introduce, for each a ∈ ℝ+, the Brownian motion associated to the distribution derivative of order a of white noise. We prove that the generator of this Markov process is the exotic Laplacian of order 2a, given by the Cesàro mean of order 2a of the second derivatives along the elements of an orthonormal basis of a suitable Hilbert space (the Cesàro space of order 2a). In particular, for a = 1/2 one finds the usual Lévy Laplacian, but also in this case the connection with the 1/2-derivative of white noise is new. The main technical tool, used to achieve these goals, is a generalization of a result due to Accardi and Smolyanov5 extending the well-known Cesàro theorem to higher order arithmetic means. These and other estimates allow to prove existence of the heat semi-group associated to any exotic Laplacian of order ≥ 1/2 and to give its explicit expression in terms of infinite dimensional Fourier transform.

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