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Structure of the Malvenuto-Reutenauer Hopf Algebra of Permutations (Extended Abstract)
Hopf algebra and algebra algebraic function
2014/12/29
We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primitive el...
Combinatorial Hopf Algebra and Generalized Dehn-Sommerville Relations
Combination of hopf algebra hopf algebra linear function generating function combination
2014/12/29
A combinatorial Hopf algebra is a graded connected Hopf algebra over a field k equipped with a character (multiplicative linear functional) : H → k. We show that the terminal object in the category ...
The algebra of quadrature formulae for generic nodes
algebra quadrature formulae generic nodes
2012/9/19
Consider the classical problem of computing the expected value of areal function fof thed-variate random variableXas a linear combination of its valuesf(z) at a finite set pointsz伕 D 伡Rd. The general ...
Representation theorem for multiply self-decomposable probability measures on generalized convolution algebra
Representation theorem multiply self-decomposable probability measures
2009/9/24
Representation theorem for multiply self-decomposable probability measures on generalized convolution algebra。
On the unconditional bundle convergence in L(2)-space over a von Neumann algebra
the unconditional bundle convergence L(2)-space a von Neumann algebra
2009/9/21
The Tandori theorem concerning the sufficient condition
for the unconditional a.e. convergence of orthogonal series is
generalized for the bundle convergence in La-space over a cr-fdte von
Neumann ...
ON THE EWGODHC HHLBEWT TRANSFORM IN L OVER A VON NEUMANN ALGEBRA
Ergodic Hilbert transform von Neumann algebra bundle convergence
2009/9/18
In this note a noncommutative version of Jajte's theorem
on the existence of the ergodic Hilbert transform is given. As
a noncommutative counterpart of the classical almost everywhere convergence
t...