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AN ALGEBRAIC CHARACTERIZATION OF COMPLETE INNER PRODUCT SPACES
, 1983
"... ABSTRACT. We present a characterization of complete inn=r product spaces using en involution on the set of all bounded linear operators on a Banach space. As a metric conditions we impose a "multiplicative " property of the norm for hermitain operators. In the second part we present a simp ..."
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simpler proof (we believe) of the Kakutani and Mackney theorem on the characterizations of complete inner product spaces. Our proof was suggested by an ingenious proof of a similar result obtained by N. Prijatelj. EY WORDS AND PHRASES. Comylete inner product spaces, an algebraic charac
Ktheory for operator algebras
 Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
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Cited by 559 (0 self)
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Neumann used the same name for Hilbert spaces in the modern sense (complete inner product spaces), which he defined in 1928. p. 3 line6: At the end of the line, 2ɛ should be 4ɛ. p. 3 I.1.2.3: The statement that a dense subspace of a Hilbert space H contains an orthonormal basis for H can be false if H
The space complexity of approximating the frequency moments
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1996
"... The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, ..."
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Cited by 855 (12 self)
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The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 780 (22 self)
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Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
Antide Sitter Space, Thermal Phase Transition, and Confinement in Gauge Theories
 Adv. Theor. Math. Phys
, 1998
"... The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super YangMills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Antide Sitter space. In this description, quantum phenome ..."
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Cited by 1087 (4 self)
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The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of N = 4 super YangMills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Antide Sitter space. In this description, quantum
Complete discrete 2D Gabor transforms by neural networks for image analysis and compression
, 1988
"... AbstractA threelayered neural network is described for transforming twodimensional discrete signals into generalized nonorthogonal 2D “Gabor ” representations for image analysis, segmentation, and compression. These transforms are conjoint spatiahpectral representations [lo], [15], which provide ..."
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Cited by 475 (8 self)
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provide a complete image description in terms of locally windowed 2D spectral coordinates embedded within global 2D spatial coordinates. Because intrinsic redundancies within images are extracted, the resulting image codes can be very compact. However, these conjoint transforms are inherently difficult
The Impact of Trade on IntraIndustry Reallocations and Aggregate Industry Productivity
, 2002
"... This paper builds a dynamic industry model with heterogeneous firms that exhibits the mechanisms by which trade causes reallocations of resources among firms in an industry. The paper shows how the exposure to trade will induce only the more productive firms to enter the export market (while some le ..."
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Cited by 1538 (24 self)
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This paper builds a dynamic industry model with heterogeneous firms that exhibits the mechanisms by which trade causes reallocations of resources among firms in an industry. The paper shows how the exposure to trade will induce only the more productive firms to enter the export market (while some
Results 1  10
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1,785,222