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458
Factoring wavelet transforms into lifting steps
 J. FOURIER ANAL. APPL
, 1998
"... This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decompositio ..."
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Cited by 584 (8 self)
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in the biorthogonal, i.e, nonunitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a waveletlike transform that maps integers to integers.
Pentagon equation and matrix bialgebras A.A.Davydov
, 2008
"... We classify coproducts on matrix algebra in terms of solutions to some modification of pentagon equation. The construction of Baaj and Skandalis describing finite dimensional unitary solutions of pentagon equation is extended to the nonunitary case. We establish the relation between HopfGalois alg ..."
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We classify coproducts on matrix algebra in terms of solutions to some modification of pentagon equation. The construction of Baaj and Skandalis describing finite dimensional unitary solutions of pentagon equation is extended to the nonunitary case. We establish the relation between Hopf
Pentagon equation and matrix bialgebras A.A.Davydov
, 2008
"... We classify coproducts on matrix algebra in terms of solutions to some modification of pentagon equation. The construction of Baaj and Skandalis describing finite dimensional unitary solutions of pentagon equation is extended to the nonunitary case. We establish the relation between HopfGalois alg ..."
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We classify coproducts on matrix algebra in terms of solutions to some modification of pentagon equation. The construction of Baaj and Skandalis describing finite dimensional unitary solutions of pentagon equation is extended to the nonunitary case. We establish the relation between Hopf
NONDISPLACEABLE LAGRANGIAN SUBMANIFOLDS AND FLOER COHOMOLOGY WITH NONUNITARY LINE BUNDLE
, 710
"... Abstract. We show that in many examples the nondisplaceability of Lagrangian submanifolds by Hamiltonian isotopy can be proved via Lagrangian Floer cohomology with nonunitary line bundle. The examples include all monotone Lagrangian torus fibers in toric Fano manifold (which was also proven by Ent ..."
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Abstract. We show that in many examples the nondisplaceability of Lagrangian submanifolds by Hamiltonian isotopy can be proved via Lagrangian Floer cohomology with nonunitary line bundle. The examples include all monotone Lagrangian torus fibers in toric Fano manifold (which was also proven
NONDISPLACEABLE LAGRANGIAN SUBMANIFOLDS AND FLOER COHOMOLOGY WITH NONUNITARY LINE BUNDLE
, 710
"... Abstract. We show that in many examples the nondisplaceability of Lagrangian submanifolds by Hamiltonian isotopy can be proved via Lagrangian Floer cohomology with nonunitary line bundle. The examples include all monotone Lagrangian torus fibers in toric Fano manifold (which was also proven by Ent ..."
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Abstract. We show that in many examples the nondisplaceability of Lagrangian submanifolds by Hamiltonian isotopy can be proved via Lagrangian Floer cohomology with nonunitary line bundle. The examples include all monotone Lagrangian torus fibers in toric Fano manifold (which was also proven
Two new gradient based nonunitary joint blockdiagonalization algorithms
 in Proc. European Signal Processing Conference (EUSIPCO’2008
, 2008
"... This paper addresses the problem of the nonunitary joint block diagonalization (NU − JBD) of a given set of matrices. Such a problem arises in various fields of applications among which blind separation of convolutive mixtures of sources and array processing for wideband signals. We present two ne ..."
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Cited by 1 (1 self)
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This paper addresses the problem of the nonunitary joint block diagonalization (NU − JBD) of a given set of matrices. Such a problem arises in various fields of applications among which blind separation of convolutive mixtures of sources and array processing for wideband signals. We present two
Nonunitary master equation for the internal state of ions traversing solids
"... Abstract We present a new method describing the time development of the internal state of fast highly charged ions subject to collisions and to spontaneous radiative decay during transport through solids. Our method describes both the buildup of coherences and the decoherence of the open quantum s ..."
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transformations of the reduced density matrix. We have developed a generalized nonunitary Lindblad form (and its Monte Carlo implementation) for the evolution in finite subspaces in which the coupling to the complement is taken into account. We use the radiative decay of a free hydrogenic atom in vacuum as a
Gravity coupled with matter and the foundation of non commutative geometry
, 1996
"... We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D i ..."
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Cited by 343 (17 self)
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We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D
UNITARY AND NONUNITARY MATRICES AS A SOURCE OF DIFFERENT BASES OF OPERATORS ACTING ON HILBERT SPACES
"... Columns of d2×N matrices are shown to create different sets of N operators acting on ddimensional Hilbert space. This construction corresponds to a formalism of the starproduct of operator symbols. The known bases are shown to be partial cases of generic formulas derived using d2×N matrices as a s ..."
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Columns of d2×N matrices are shown to create different sets of N operators acting on ddimensional Hilbert space. This construction corresponds to a formalism of the starproduct of operator symbols. The known bases are shown to be partial cases of generic formulas derived using d2×N matrices as a
Truncations of random unitary matrices Karol ˙Zyczkowski† ‡ and HansJürgen Sommers§
, 1999
"... Abstract. We analyse properties of nonHermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N> M, distributed according to the Haar measure. In this way we define ensembles of random matrices and study the statistical properties of the spe ..."
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of the spectrum located inside the unit circle. In the limit of large matrices, this ensemble is characterized by the ratio M=N. For the truncated CUE we analytically derive the joint density of eigenvalues and all correlation functions. In the strongly nonunitary case universal Ginibre behaviour is found. For N
Results 1  10
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458