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Extensions of Lipschitz mappings into Hilbert space
, 1984(Here ll&lltip is the Lipschitz constant of the function g.) A classical result of Kirszbraun's [14, p. 48] states that L(t2, n) = 1 for all n, but it is easy to see that L(X, n) ~ ~ as n ~ ~ for many metric spaces X. Marcus and Pisier [10] initiated the
W. Johnson, J. Lindenstrauss
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Theory of linear operators in Hilbert space
, 1961linear operators in hilbert spaces | springerlink abstract. we recall some fundamental notions of the theory of linear operators in hilbert spaces which are required for a rigorous formulation of the rules of quantum mechanics in the one-body case.
N. Akhiezer, I. M. Glazman
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Hyperbolic Hilbert space [PDF]
Advances in Applied Clifford Algebras, 2000 Let \(H\) be the hyperbolic complex plane and let \(\Xi\) be the divisors of zero region. An addition sub-semi-group \(S\) of \(H\) is called hyperbolic semi-linear space if \(o\in S\) and there exists an operation of multiplication by non-negative real numbers having the following properties: 1. \((ab)X = a(bX)\) 2. \((a+b)X = aX + bX\); 3. \(a(X+Y) =
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Behavioral and Brain Sciences, 2013
AbstractUse of quantum probability as a top-down model of cognition will be enhanced by consideration of the underlying complex-valued wave function, which allows a better account of interference effects and of the structure of learned and ad hoc question operators.
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AbstractUse of quantum probability as a top-down model of cognition will be enhanced by consideration of the underlying complex-valued wave function, which allows a better account of interference effects and of the structure of learned and ad hoc question operators.
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Ukrainian Mathematical Journal, 1986
We continue the study of the structure of families of probability measures, started by \textit{I. Sh. Ibramkhalilov} and \textit{A. V. Skorokhod} [Estimates of parameters of stochastic processes (1980; Zbl 0429.60031)] and \textit{Z. S. Zerakidze} [Soobshch. Akad. Nauk Gruz. SSR 113, 37-39 (1984; Zbl 0562.60002)].
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We continue the study of the structure of families of probability measures, started by \textit{I. Sh. Ibramkhalilov} and \textit{A. V. Skorokhod} [Estimates of parameters of stochastic processes (1980; Zbl 0429.60031)] and \textit{Z. S. Zerakidze} [Soobshch. Akad. Nauk Gruz. SSR 113, 37-39 (1984; Zbl 0562.60002)].
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1964
Publisher Summary This chapter focuses on Hilbert space. The chapter discusses the theory of bounded operators, and reviews the orthogonality and orthogonal systems of elements. Various theorems are proven. Linear operators, and bilinear and quadratic functionals are reviewed. The chapter reviews bounds of a self-conjugate operator.
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Publisher Summary This chapter focuses on Hilbert space. The chapter discusses the theory of bounded operators, and reviews the orthogonality and orthogonal systems of elements. Various theorems are proven. Linear operators, and bilinear and quadratic functionals are reviewed. The chapter reviews bounds of a self-conjugate operator.
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2003
The main feature of a basis \(\{f_{k}\}_{k=1}^{\infty }\) in a Hilbert space \(\mathcal{H}\) is that every \(f \in \mathcal{H}\) can be represented as a superposition of the elements f k in the basis: $$\displaystyle\begin{array}{rcl} f =\sum _{ k=1}^{\infty }c_{ k}(f)f_{k}.& &{}\end{array}$$ (5.1) The coefficients c k (f) are unique.
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The main feature of a basis \(\{f_{k}\}_{k=1}^{\infty }\) in a Hilbert space \(\mathcal{H}\) is that every \(f \in \mathcal{H}\) can be represented as a superposition of the elements f k in the basis: $$\displaystyle\begin{array}{rcl} f =\sum _{ k=1}^{\infty }c_{ k}(f)f_{k}.& &{}\end{array}$$ (5.1) The coefficients c k (f) are unique.
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Harmonic Analysis of Operators on Hilbert Space
, 1970B. Szőkefalvi-Nagy +3 more
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1966
Hilbert space is a special case of Banach space, but it deserves separate consideration because of its importance in applications. In Hilbert spaces the general results deduced in previous chapters are strengthened and, at the same time, new problems arise.
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Hilbert space is a special case of Banach space, but it deserves separate consideration because of its importance in applications. In Hilbert spaces the general results deduced in previous chapters are strengthened and, at the same time, new problems arise.
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Strong convergence result for solving monotone variational inequalities in Hilbert space
Numerical Algorithms, 2018Jun Yang, Hongwei Liu
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