The decomposition of matrix-valued measures.

Decomposition of group-valued measures on orthoalgebras

We present a general decomposition theorem for a positive inner regular finitely additive measure on an orthoalgebra L with values in an ordered topological group G, not necessarily commutative. In the case where L is a Boolean algebra, we establish the uniqueness of such a decomposition. With mild extra hypotheses on G, we extend this Boolean decomposition, preserving the uniqueness, to the ca...

determinant of the hankel matrix with binomial entries

abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.

The theory of matrix-valued multiresolution analysis frames

Orthogonal vs. Non-Orthogonal Reducibility of Matrix-Valued Measures

A matrix-valued measure Θ reduces to measures of smaller size if there exists a constant invertible matrix M such that MΘM∗ is block diagonal. Equivalently, the real vector space A of all matrices T such that TΘ(X) = Θ(X)T ∗ for any Borel set X is nontrivial. If the subspace Ah of self-adjoints elements in the commutant algebra A of Θ is nontrivial, then Θ is reducible via a unitary matrix. In ...

the theory of matrix-valued multiresolution analysis frames

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