Halmos, P.R., 1951. Introduction to Hilbert Space and The Theory of Spectral Multiplicity. Chelsea Publishing, New York. Home/Search Document Not in Database Summary Related Articles Check |
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Relationships between Gaussian processes, Support Vector machines .. - Seeger (2000) (Correct)
....spaces, the inherent geometry of the embedding of input into feature space is an important concept when working with kernel methods. We cannot discuss feature space geometry in detail here, but refer to [5] for further reading. 3. 1 Some facts from Hilbert space theory A Hilbert space (see [18]) is a complete vector space (complete spaces are also called Banach spaces) with an inner product induced by the norm of the space. A normed vector space is complete if every Cauchy sequence in the space converges against an element of the space. Note that any inner product space can be completed ....
P. Halmos. Introduction to Hilbert Space and the Theory of Spectral Multiplicity. Chelsea, New York, 1957.
Generalized Multiresolution Analyses, and a Construction .. - Baggett, Medina, Merrill (1998) (2 citations) (Correct)
....of Gamma determined by its action on V 1 and W 0 respectively. We next employ some tools from abstract harmonic analysis. By the spectral theorem for commutative groups, the representation ae can be decomposed as a direct integral over b Gamma, the group of characters of Gamma. See e.g. M] [Ha], He] More precisely, there exists a unique projection valued measure p on b Gamma for which ae fl = Z b Gamma fl( dp( The representation ae 0 is similarly determined by a projection valued measure p 0 on b Gamma. We will analyze ae by letting Gamma act on both sides of the ....
....0 and ae ffi ff of Gamma are unitarily equivalent. Thus the projection valued measure p 0 is unitarily equivalent to ff (p) The equivalence of ae 0 to the direct integral above then follows. By the spectral multiplicity theory developed by Stone [S] and Mackey [M] see also [He] and [Ha]) the projection valued measure p is completely determined by a measure class [ on b Gamma, and a multiplicity function m mapping b Gamma into the set f0; 1; 2; 1g: This multiplicity function roughly counts the number of times each character occurs in the representation ae. ....
Paul Halmos, Introduction to Hilbert Space and the Theory of Spectral Multiplicity, Chelsea Publishing Co., New York, 1951.
Non-causality: The role of the omitted variables - Triacca (1998) (Correct)
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Halmos, P.R., 1951. Introduction to Hilbert Space and The Theory of Spectral Multiplicity. Chelsea Publishing, New York.
Gaussian Processes for Machine Learning - Seeger (2004) (Correct)
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P. Halmos. Introduction to Hilbert Space and the Theory of Spectral Multiplicity. Chelsea, New York, 1957.
The Action of Translations on Wavelet Subspaces - Weber (1999) (Correct)
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P. Halmos, Introduction to Hilbert Space and The Theory of Spectral Multiplicity, Chelsea, New York.
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