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Spectral Measures
"... The theory of spectra for Banach algebras is outlined, including the GelfandNaǐmark theorem for commutative B ∗algebras. Resolutions of the identity are introduced, with examples; finally, we prove the spectral theorem for bounded normal operators on a Hilbert space, and conclude with some applica ..."
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The theory of spectra for Banach algebras is outlined, including the GelfandNaǐmark theorem for commutative B ∗algebras. Resolutions of the identity are introduced, with examples; finally, we prove the spectral theorem for bounded normal operators on a Hilbert space, and conclude with some
Spectral Measures and Spectral Families
"... ABSTRACT: We focus here on some very recent results and its studies. Our main contribution is to provide some numerical and empirical facts concerning spectral Measures and Spectral Families. I. ..."
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ABSTRACT: We focus here on some very recent results and its studies. Our main contribution is to provide some numerical and empirical facts concerning spectral Measures and Spectral Families. I.
Some properties of spectral measures
 Appl. Comput. Harmon. Anal
, 2006
"... Abstract. A Borel measure µ in R d is called a spectral measure if there exists a set Λ ⊂ R d such that the set of exponentials {exp(2πiλ · x) : λ ∈ Λ} forms an orthogonal basis for L 2 (µ). In this paper we prove some properties of spectral measures. In particular, we prove results that highlight t ..."
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Cited by 7 (0 self)
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Abstract. A Borel measure µ in R d is called a spectral measure if there exists a set Λ ⊂ R d such that the set of exponentials {exp(2πiλ · x) : λ ∈ Λ} forms an orthogonal basis for L 2 (µ). In this paper we prove some properties of spectral measures. In particular, we prove results that highlight
ON THE GROWTH OF THE SPECTRAL MEASURE
, 1992
"... ABSTRACT. We are concerned with the asymptotics of the spectral measure associated with a selfadjoint operator. By using comparison techniques we shall show that the eigenfunctionals of L2 are close to the eigenfunctionals L1 if and only if dr1 dF2 as A oo. ..."
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ABSTRACT. We are concerned with the asymptotics of the spectral measure associated with a selfadjoint operator. By using comparison techniques we shall show that the eigenfunctionals of L2 are close to the eigenfunctionals L1 if and only if dr1 dF2 as A oo.
SPECTRAL MEASURES AND MOMENT PROBLEMS
 SPECTRAL THEORY AND ITS APPLICATIONS THETA 2003, PAGES 173215
, 2003
"... In this expository paper we try to emphasize some connections between functional analysis, in particular operator theory, and moment problems. A central role in this discussion is played by the operatorvalued positive measures, in particular the spectral measures, which are mathematical objects r ..."
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In this expository paper we try to emphasize some connections between functional analysis, in particular operator theory, and moment problems. A central role in this discussion is played by the operatorvalued positive measures, in particular the spectral measures, which are mathematical objects
An approach to correlate tandem mass spectral data of peptides with amino acid sequences in a protein database
 J. Am. Soc. Mass Spectrom
, 1994
"... A method to correlate the uninterpreted tandem mass spectra of peptides produced under low energy (lo50 eV) collision conditions with amino acid sequences in the Genpept database has been developed. In this method the protein database is searched to identify linear amino acid sequences within a mas ..."
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Cited by 932 (19 self)
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mass tolerance of * 1 u of the precursor ion molecular weight. A crosscorrelation function is then used to provide a measurement of similarity between the masstocharge ratios for the fragment ions predicted from amino acid sequences obtained from the database and the fragment ions observed
Portfolio Optimization with Spectral Measures of Risk
, 2008
"... We study Spectral Measures of Risk from the perspective of portfolio optimization. We derive exact results which extend to general Spectral Measures Mφ the Pflug–Rockafellar–Uryasev methodology for the minimization of α–Expected Shortfall. The minimization problem of a spectral measure is shown to b ..."
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Cited by 27 (0 self)
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We study Spectral Measures of Risk from the perspective of portfolio optimization. We derive exact results which extend to general Spectral Measures Mφ the Pflug–Rockafellar–Uryasev methodology for the minimization of α–Expected Shortfall. The minimization problem of a spectral measure is shown
Concentration of the Spectral Measure for Large Matrices
 ELECTRONIC COMMUNICATIONS IN PROBABILITY
, 2000
"... We derive concentration inequalities for functions of the empirical measure of eigenvalues for large, random, self adjoint matrices, with not necessarily Gaussian entries. The results presented apply in particular to nonGaussian Wigner and Wishart matrices. We also provide concentration bounds fo ..."
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Cited by 99 (13 self)
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We derive concentration inequalities for functions of the empirical measure of eigenvalues for large, random, self adjoint matrices, with not necessarily Gaussian entries. The results presented apply in particular to nonGaussian Wigner and Wishart matrices. We also provide concentration bounds
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 494 (0 self)
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number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong
Results 1  10
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