The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Zsigmond Tarcsay - One of the best experts on this subject based on the ideXlab platform.
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Radon–Nikodym Theorems for Nonnegative Forms, Measures and Representable Functionals
Complex Analysis and Operator Theory, 2014Co-Authors: Zsigmond TarcsayAbstract:The aim of this paper is to establish two Radon–Nikodym-type theorems for nonnegative Hermitian forms defined on a real or Complex Vector Space and to apply these results to provide some known Radon–Nikodym-type theorems of the theory of representable positive functionals, \(\sigma \)-additive and finitely additive measures.
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Radon-Nikodym theorems for nonnegative forms, measures and representable functionals
arXiv: Functional Analysis, 2014Co-Authors: Zsigmond TarcsayAbstract:The aim of this note is to establish two Radon--Nikodym type theorems for nonnegative Hermitian forms defined on a real or Complex Vector Space. We apply these results to prove the known Radon--Nikodym theorems of the theory of representable positive functionals, $\sigma$-additive and finitely additive measures.
Judit Abardia - One of the best experts on this subject based on the ideXlab platform.
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minkowski valuations in a 2 dimensional Complex Vector Space
International Mathematics Research Notices, 2015Co-Authors: Judit AbardiaAbstract:The classification of continuous, translation invariant Minkowski valuations which are contravariant (or covariant) with respect to the Complex special linear group is established in a 2-dimensional Complex Vector Space. Every such valuation is given by the sum of a valuation of degree of homogeneity 1 and 3. In dimensions $m\geq 3$ such a classification was previously established and only valuations of a degree of homogeneity 2m-1 appear.
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Difference bodies in Complex Vector Spaces
Journal of Functional Analysis, 2012Co-Authors: Judit AbardiaAbstract:Abstract A complete classification is obtained of continuous, translation invariant, Minkowski valuations on an m -dimensional Complex Vector Space which are covariant under the Complex special linear group.
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Projection bodies in Complex Vector Spaces
Advances in Mathematics, 2011Co-Authors: Judit Abardia, Andreas BernigAbstract:The Space of Minkowski valuations on an m-dimensional Complex Vector Space which are continuous, translation invariant and contravariant under the Complex special linear group is explicitly described. Each valuation with these properties is shown to satisfy geometric inequalities of the Brunn–Minkowski, Aleksandrov–Fenchel and Minkowski type.
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Projection bodies in Complex Vector Spaces
arXiv: Differential Geometry, 2011Co-Authors: Judit Abardia, Andreas BernigAbstract:The Space of Minkowski valuations on an m-dimensional Complex Vector Space which are continuous, translation invariant and contravariant under the Complex special linear group is explicitly described. Each valuation with these properties is shown to satisfy geometric inequalities of Brunn-Minkowski, Aleksandrov-Fenchel and Minkowski type.
Andreas Bernig - One of the best experts on this subject based on the ideXlab platform.
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Projection bodies in Complex Vector Spaces
Advances in Mathematics, 2011Co-Authors: Judit Abardia, Andreas BernigAbstract:The Space of Minkowski valuations on an m-dimensional Complex Vector Space which are continuous, translation invariant and contravariant under the Complex special linear group is explicitly described. Each valuation with these properties is shown to satisfy geometric inequalities of the Brunn–Minkowski, Aleksandrov–Fenchel and Minkowski type.
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Projection bodies in Complex Vector Spaces
arXiv: Differential Geometry, 2011Co-Authors: Judit Abardia, Andreas BernigAbstract:The Space of Minkowski valuations on an m-dimensional Complex Vector Space which are continuous, translation invariant and contravariant under the Complex special linear group is explicitly described. Each valuation with these properties is shown to satisfy geometric inequalities of Brunn-Minkowski, Aleksandrov-Fenchel and Minkowski type.
Reinhold Haeb-umbach - One of the best experts on this subject based on the ideXlab platform.
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Blind speech separation employing directional statistics in an Expectation Maximization framework
2010 IEEE International Conference on Acoustics Speech and Signal Processing, 2010Co-Authors: Dang Hai Tran Vu, Reinhold Haeb-umbachAbstract:In this paper we propose to employ directional statistics in a Complex Vector Space to approach the problem of blind speech separation in the presence of spatially correlated noise. We interpret the values of the short time Fourier transform of the microphone signals to be draws from a mixture of Complex Watson distributions, a probabilistic model which naturally accounts for spatial aliasing. The parameters of the density are related to the a priori source probabilities, the power of the sources and the transfer function ratios from sources to sensors. Estimation formulas are derived for these parameters by employing the Expectation Maximization (EM) algorithm. The E-step corresponds to the estimation of the source presence probabilities for each time-frequency bin, while the M-step leads to a maximum signal-to-noise ratio (MaxSNR) beamformer in the presence of uncertainty about the source activity. Experimental results are reported for an implementation in a generalized sidelobe canceller (GSC) like spatial beamforming configuration for 3 speech sources with significant coherent noise in reverberant environments, demonstrating the usefulness of the novel modeling framework.
Adriaan C. Zaanen - One of the best experts on this subject based on the ideXlab platform.
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Normed Riesz Spaces and Banach Lattices
Introduction to Operator Theory in Riesz Spaces, 1997Co-Authors: Adriaan C. ZaanenAbstract:Let V be a real or Complex Vector Space and assume that to each element f ∈ V there is assigned a real number ‖ f ‖ such that
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Complex Riesz Spaces
Introduction to Operator Theory in Riesz Spaces, 1997Co-Authors: Adriaan C. ZaanenAbstract:All Riesz Spaces in the preceding sections are real Riesz Spaces. We shall now define Complex Riesz Spaces and then extend a considerable part of the theory to these Complex Spaces. Recall first that the Cartesian product X × Y of the non-empty sets X and Y is the set of all ordered pairs (x, y) such that x ∈ X and y ∈ Y. In the case that X = Y = V, where V is a real Vector Space, we can equip the Cartesian product V × V with a Vector Space structure by defining $$ \left( {{f_1},{g_1}} \right) + \left( {{f_2},{g_2}} \right) = \left( {{f_1} + {f_2},{g_1} + {g_2}} \right), $$ $$ \left( {\alpha + i\beta } \right)\left( {f,g} \right) = \left( {\alpha f - \beta g,\beta f + \alpha g} \right) for\alpha ,\beta real numbers, $$ and the so defined Complex Vector Space is denoted by V + iV. Note that (f,0) + (g,0) = (f + g,0) and α(f,0)=(αf,0) for α real. Hence, identifying f ∈ V and (f,0)∈ V + iV, the Space V is embedded in V + iV as a real-linear subSpace. Note also that i(g, 0) = (0, g) by the above definition, so $$ \left( {f,g} \right) = \left( {f,0} \right) + \left( {0,g} \right) = \left( {f,0} \right) + i\left( {g,0} \right). $$