نتایج جستجو برای: hilbert matrix

تعداد نتایج: 387624  

Journal: :Zeitschrift für Analysis und ihre Anwendungen 2008

2003
Maciej M. Duras

The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the systems act on these Hilbert spaces and they are treated as random matrices in generic bases of the eigenfunctions. The random e...

Journal: :Open Syst. Inform. Dynam. 2007
Janusz Grabowski Marek Kus Giuseppe Marmo

Relations between states and maps, which are known for quantum systems in finite-dimensional Hilbert spaces, are formulated rigorously in geometrical terms with no use of coordinate (matrix) interpretation. In a tensor product realization they are represented simply by a permutation of factors. This leads to natural generalizations for infinite-dimensional Hilbert spaces and a simple proof of a...

2005
TSUYOSHI ANDO TOMOHIRO HAYASHI

We will show that for any two bounded linear operators X, Y on a Hilbert space H, if they satisfy the triangle equality |X + Y | = |X | + |Y |, there exists a partial isometry U on H such that X = U |X | and Y = U |Y |. This is a generalization of Thompson’s theorem to the matrix case proved by using a trace. 47A05, 47A10, 47A12 operator theory, Hilbert space, triangle inequality

2002
Maciej M. Duras

1 Abstract The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the systems act on these Hilbert spaces and they are treated as random matrices in generic bases of the eigenfunctions. T...

2001
Maciej M. Duras

The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the systems act on these Hilbert spaces and they are treated as random matrices in generic bases of the eigenfunctions. The random eigenproblems are presented and so...

Journal: :CSSP 2014
Subhash C. Kak

Abstract This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being zero and non-zero. Specific examples for 4point, 6-point, and 8-point NHT are provided. The NHT transformation can be used as a primitive to create cry...

2005
HEE OH

We discuss an open problem on the discreteness of subgroups of (SL2(R)) (n ≥ 2) generated by n linearly independent upper triangular matrices and n linearly independent lower triangular matrices. According to a conjecture by Margulis, only Hilbert modular groups can arise this way. The purpose of this note is to explain how this open problem is related to another conjecture on the orbit behavio...

2007
Pachara Chaisuriya Sing-Cheong Ong Sheng-Wang Wang Aloys Krieg

Let be a C∗-algebra with identity 1, and let s( ) denote the set of all states on . For p,q,r ∈ [1,∞), denote by r( ) the set of all infinite matrices A= [ajk]j,k=1 over such that the matrix (φ[A[2]]) [r] := [(φ(ajkajk))]j,k=1 defines a bounded linear operator from p to q for all φ∈ s( ). Then r( ) is a Banach algebra with the Schur product operation and norm ‖A‖ = sup{‖(φ[A[2]])‖ : φ∈ s( )}. A...

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