منابع مشابه
Fredholm Determinant for Piecewise Linear Transformations
We call the number ξ the lower Lyapunov number. We will study Spec^) , the spectrum of P \BV> the restriction of P to the subspace BV of functions with bounded variation. The generating function of P is determined by the orbits of the division points of the partition, and the orbits are characterized by a finite dimensional matrix Φ(z) which is defined by a renewal equation (§ 3). Hence, we can...
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In this paper we propose a framework for supervised and semi-supervised learning based on reformulating the learning problem as a regularized Fredholm integral equation. Our approach fits naturally into the kernel framework and can be interpreted as constructing new data-dependent kernels, which we call Fredholm kernels. We proceed to discuss the “noise assumption” for semi-supervised learning ...
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Let H be a Hilbert space with an inner product that is conjugate linear in the first variable. We do not presume unless we say so that H is separable. We denote by B(H) the set of bounded linear operators H → H. For any A ∈ B(H), A∗A is positive and one proves that it has a unique positive square root |A| ∈ B(H). We call |A| the absolute value of A. We say that U ∈ B(H) is a partial isometry if...
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(2) If K ∈ B(X) is compact, then for all λ ∈ C \ {0}, K − λ1 is Fredholm with index zero. (3) The shift operator S± ∈ B(`p) for 1 ≤ p ≤ ∞ defined by (S±x)n = xn±1 is Fredholm with index ±1. (4) If X,Y are finite dimensional and T ∈ B(X,Y ), then by the Rank-Nullity Theorem, ind(T ) = dim(X)− dim(Y ). Lemma 3. Suppose E,F ⊆ X are closed subspaces with F finite dimensional. (1) The subspace E + F...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1984
ISSN: 0263-6115
DOI: 10.1017/s1446788700021765