Abstract In this paper we study $$L_2$$ L 2 -norm sampling discretization and recovery of complex-valued functions in RKHS on $$D \subset \mathbb {R}^d$$ D ⊂ R d </mml:...

Emmanuel Preissmann, Olivier Lévêque Swiss Federal Institute of Technology Lausanne, Switzerland Abstract In this paper, we study spectral properties of generalized weighted Hilbert matrices. In particular, we establish results on the spectral norm, determinant, as well as various relations between the eigenvalues and eigenvectors of such matrices. We also study the asymptotic behaviour of the ...

In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy bo...

By the method of weight coefficients and techniques of real analysis, a Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. The equivalent forms, the operator expressions with the norm, the reverses and some particular examples are also considered.

In this short note, we extend the celebrated results of Tao and Vu, Krishnapur on universality empirical spectral distributions to a wide class inhomogeneous complex random matrices, by showing that technical hard-to-verify Fourier domination assumption may be replaced simply natural uniform anti-concentration assumption. Along way, show whose expected squared Hilbert-Schmidt norm is quadrati...

Inverse formulas for the tensor product are used to develop an algorithm to compute Schmidt decompositions of Finite Schmidt Rank (FSR) bounded operators on the tensor product of separable Hilbert spaces. The algorithm is then applied to solve inverse problems related to the tensor product of bounded operators. In particular, we show how properties of a FSR bounded operator are reflected by the...

X iv :q ua nt -p h/ 06 05 07 9 v1 8 M ay 2 00 6 Geometrical aspects of entanglement Jon Magne Leinaas, Jan Myrheim and Eirik Ovrum (a) Department of Physics, University of Oslo, P.O. Box 1048 Blindern, 0316 Oslo, Norway (b) Centre of Mathematics for Applications, P.O. Box 1053 Blindern, 0316 Oslo, Norway and (c) Department of Physics, The Norwegian University of Science and Technology, 7491 Tro...

in this paper, a numerical scheme for solving singular initial/boundary value problems presented.by applying the reproducing kernel hilbert space method (rkhsm) for solving these problems,this method obtained to approximated solution. numerical examples are given to demonstrate theaccuracy of the present method. the result obtained by the method and the exact solution are foundto be in good agr...