Conjugate Space of PC[0,1]

2019 ◽  
Vol 09 (05) ◽  
pp. 641-646
Author(s):  
慧 温
Keyword(s):  
Conjugate Space

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

On a Theorem of Beurling and Livingston

1965 ◽  
Vol 17 ◽  
pp. 367-372 ◽  
Author(s):  
Felix E. Browder
Keyword(s):  
Banach Space ◽  
Fourier Series ◽  
Banach Spaces ◽  
General Result ◽  
Functional Equations ◽  
Linear Functional ◽  
Monotone Mappings ◽  
Conjugate Space ◽  
Non Linear ◽  
Duality Mappings

In their paper (1), Beurling and Livingston established a generalization of the Riesz-Fischer theorem for Fourier series in Lp using a theorem on duality mappings of a Banach space B into its conjugate space B*. It is our purpose in the present paper to give another proof of this theorem by deriving it from a more general result concerning monotone mappings related to recent results on non-linear functional equations in Banach spaces obtained by the writer (2, 3, 4, 5) and G. J. Minty (6).

scholarly journals On certain subalgebras of a dual B*-algebra

1977 ◽  
Vol 23 (1) ◽  
pp. 105-111 ◽  
Author(s):  
Pak-Ken Wong
Keyword(s):  
Conjugate Space

Let A be a dual B*-algebra and Ap the p-class in A. We show that the conjugate space of A1 is A**, the second conjugate space of A. We also obtain a three lines theorem for Ap (1 ≦p≦∞).

scholarly journals On a Class of Metrical Automorphisms on Gaussian Measure Space

1970 ◽  
Vol 38 ◽  
pp. 21-25 ◽  
Author(s):  
Hisao Nomoto
Keyword(s):  
Gaussian Measure ◽  
Measure Space ◽  
Nuclear Space ◽  
Infinite Dimensional ◽  
Conjugate Space

Let E be an infinite dimensional real nuclear space and H be its completion by a continuous Hilbertian norm ║ ║ of E. Then we have the relationwhere E* is the conjugate space of E. Consider a function C(ξ) on E defined by the formula(1)

Gowers-Maurey’ s space and its conjugate space

1997 ◽  
Vol 42 (1) ◽  
pp. 14-17
Author(s):  
Huaijie Zhong
Keyword(s):  
Conjugate Space

The Second Conjugates of Certain Banach Algebras

1975 ◽  
Vol 27 (5) ◽  
pp. 1029-1035 ◽  
Author(s):  
Pak-Ken Wong
Keyword(s):  
Recent Result ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Arens Product ◽  
Conjugate Space ◽  
Natural Extensions ◽  
Semisimple Banach Algebra

Let A be a Banach algebra and A** its second conjugate space. Arens has denned two natural extensions of the product on A to A**. Under either Arens product, A** becomes a Banach algebra. Let A be a semisimple Banach algebra which is a dense two-sided ideal of a B*-algebra B and R** the radical of (A**, o). We show that A** = Q ⊕ R**, where Q is a closed two-sided ideal of A**, o). This was inspired by Alexander's recent result for simple dual A*-algebras (see [1, p. 573, Theorem 5]). We also obtain that if A is commutative, then A is Arens regular.

scholarly journals On the problem of non-smoothness of non-reflexive second conjugate spaces

1975 ◽  
Vol 12 (3) ◽  
pp. 407-416 ◽  
Author(s):  
Ivan Singer
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Linear Subspace ◽  
Canonical Embedding ◽  
Reflexive Banach Spaces ◽  
Closed Linear Subspace ◽  
Conjugate Space ◽  
The Family

We prove that if E is a Banach space which has a subspace G such that the conjugate space G* contains a proper norm closed linear subspace V of characteristic 1, then E** is not smooth and there exist in πE(E) points of non-smoothness for E**, where πE: E → E** is the canonical embedding. We show that the spaces E having such a subspace G constitute a large proper subfamily of the family of all non-reflexive Banach spaces.

MIGRATION BY FOURIER TRANSFORM

Geophysics ◽  
1978 ◽  
Vol 43 (1) ◽  
pp. 23-48 ◽  
Author(s):  
R. H. Stolt
Keyword(s):  
Fourier Transform ◽  
Wave Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Three Dimensional ◽  
Frequency Dispersion ◽  
Scalar Wave ◽  
Conjugate Space ◽  
And Migration

Wave equation migration is known to be simpler in principle when the horizontal coordinate or coordinates are replaced by their Fourier conjugates. Two practical migration schemes utilizing this concept are developed in this paper. One scheme extends the Claerbout finite difference method, greatly reducing dispersion problems usually associated with this method at higher dips and frequencies. The second scheme effects a Fourier transform in both space and time; by using the full scalar wave equation in the conjugate space, the method eliminates (up to the aliasing frequency) dispersion altogether. The second method in particular appears adaptable to three‐dimensional migration and migration before stack.

Integral Functionals in the Duals of Lλ-Spacesc(1)

1972 ◽  
Vol 15 (4) ◽  
pp. 489-499 ◽  
Author(s):  
H. W. Ellis ◽  
J. D. Hiscocks
Keyword(s):  
Vector Space ◽  
Function Spaces ◽  
Length Function ◽  
Integral Functionals ◽  
Conjugate Space ◽  
Image Position

Luxemburg and Zaanen [5] call an element φ of the topological dual of a normed or seminormed vector space V an integral ifWe denote the space of integrals by VI, For the Lλ function spaces introduced by Ellis and Halperin [2] another Banach subspace of the dual emerges, namely the conjugate space Lλ* which is the Lλ space determined by the conjugate length function λ*-Lλ* is contained in (Lλ)I but need not coincide with it.

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