The Experts below are selected from a list of 243 Experts worldwide ranked by ideXlab platform
Francesca Antoci - One of the best experts on this subject based on the ideXlab platform.
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on the spectrum of the laplace beltrami operator for p forms for a class of warped product metrics
Advances in Mathematics, 2004Co-Authors: Francesca AntociAbstract:We explicitly compute the essential spectrum of the Laplace–Beltrami operator for p-forms for the class of warped product metrics dσ2=y2ady2+y2bdθ∂M2, where y is a boundary Defining Function on a compact manifold with boundary M.
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on the spectrum of the laplace beltrami operator for p forms for a class of warped product metrics
arXiv: Spectral Theory, 2003Co-Authors: Francesca AntociAbstract:We explicitely compute the essential spectrum of the Laplace-Beltrami operator for $p$-forms for the class of warped product metrics $d\sigma^2= y^{2a}dy^2 + y^{2b}d\theta_{\partial M}^2$, where $y$ is a boundary Defining Function on a compact manifold with boundary $M$.
Vladimir Bolotnikov - One of the best experts on this subject based on the ideXlab platform.
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realization and interpolation for schur agler class Functions on domains with matrix polynomial Defining Function in cn
Journal of Functional Analysis, 2004Co-Authors: Joseph A Ball, Vladimir BolotnikovAbstract:Abstract We consider a bitangential interpolation problem for operator-valued Functions defined on a general class of domains in C n (including as particular cases, Cartan domains of types I–III) which satisfy a type of von Neumann inequality associated with the domain. We show that any such Function has a realization in terms of a unitary colligation and the Defining polynomial for the domain. We show how the solution of various classes of bitangential interpolation problems for this class of Functions corresponds to a unitary extension of a particular partially defined isometry uniquely specified by the interpolation data. Criteria for existence of solutions are given (1) in terms of positivity of a certain kernel completely determined by the data, or, more generally, (2) by the existence of a positive-kernel solution of a certain generalized Stein equation completely determined by the data.
Anne-katrin Herbig - One of the best experts on this subject based on the ideXlab platform.
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A note on plurisubharmonic Defining Functions in {\mathbb{C}^{n}}
Mathematische Annalen, 2008Co-Authors: John Erik Fornæss, Anne-katrin HerbigAbstract:Let \({\Omega\subset\subset\mathbb{C}^{n}}\) , n ≥ 3, be a smoothly bounded domain. Suppose that Ω admits a smooth Defining Function which is plurisubharmonic on the boundary of Ω. Then a Diederich–Fornaess exponent can be chosen arbitrarily close to 1, and the closure of Ω admits a Stein neighborhood basis.
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A note on plurisubharmonic Defining Functions in $\mathbb{C}^n$
arXiv: Complex Variables, 2007Co-Authors: John Erik Fornæss, Anne-katrin HerbigAbstract:Let D be a smoothly bounded domain in complex space of dimension larger than 2. Suppose that D admits a smooth Defining Function which is plurisubharmonic on the boundary of D. Then the Diederich-Fornaess exponent can be chosen arbitrarily close to 1, and the closure of D admits a Stein neighborhood basis.
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A note on plurisubharmonic Defining Functions in$$\mathbb{C}^2$$
Mathematische Zeitschrift, 2007Co-Authors: John Erik Fornæss, Anne-katrin HerbigAbstract:Let Ω ⊂⊂ \(\mathbb{C}^2\) be a smoothly bounded domain. Suppose that Ω admits a smooth Defining Function which is plurisubharmonic on the boundary of Ω. Then the Diederich-Fornaess exponent can be chosen arbitrarily close to 1, and the closure of Ω admits a Stein neighborhood basis.
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A note on plurisubharmonic Defining Functions in C^2
arXiv: Complex Variables, 2006Co-Authors: John Erik Fornæss, Anne-katrin HerbigAbstract:Let D be a smoothly bounded domain in C^2. Suppose that D admits a smooth Defining Function which is plurisubharmonic on the boundary of D. Then the Diederich-Fornaess exponent can be chosen arbitrarily close to 1, and the closure of D admits a Stein neighborhood basis.
A K B Chand - One of the best experts on this subject based on the ideXlab platform.
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A $\mathcal{C}^{1}$ -Rational Cubic Fractal Interpolation Function: Convergence and Associated Parameter Identification Problem
Acta Applicandae Mathematicae, 2015Co-Authors: Pragasam Viswanathan, A K B ChandAbstract:This paper introduces a rational Fractal Interpolation Function (FIF), in the sense that it is obtained using a rational cubic spline transformation involving two shape parameters, and investigates its applicability in some constrained interpolation problems. We identify suitable values for the parameters of the corresponding Iterated Function System (IFS) so that it generates positive rational FIFs for a given set of positive data. Further, the problem of identifying the rational IFS parameters so as to ensure that its attractor (graph of the corresponding rational FIF) lies in a specified rectangle is also addressed. With the assumption that the data Defining Function is continuously differentiable, an upper bound for the interpolation error (with respect to the uniform norm) for the rational FIF is obtained. As a consequence, the uniform convergence of the rational FIF to the original Function as the norm of the partition tends to zero is proven.
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a mathcal c 1 rational cubic fractal interpolation Function convergence and associated parameter identification problem
Acta Applicandae Mathematicae, 2015Co-Authors: Pragasam Viswanathan, A K B ChandAbstract:This paper introduces a rational Fractal Interpolation Function (FIF), in the sense that it is obtained using a rational cubic spline transformation involving two shape parameters, and investigates its applicability in some constrained interpolation problems. We identify suitable values for the parameters of the corresponding Iterated Function System (IFS) so that it generates positive rational FIFs for a given set of positive data. Further, the problem of identifying the rational IFS parameters so as to ensure that its attractor (graph of the corresponding rational FIF) lies in a specified rectangle is also addressed. With the assumption that the data Defining Function is continuously differentiable, an upper bound for the interpolation error (with respect to the uniform norm) for the rational FIF is obtained. As a consequence, the uniform convergence of the rational FIF to the original Function as the norm of the partition tends to zero is proven.
Joseph A Ball - One of the best experts on this subject based on the ideXlab platform.
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realization and interpolation for schur agler class Functions on domains with matrix polynomial Defining Function in cn
Journal of Functional Analysis, 2004Co-Authors: Joseph A Ball, Vladimir BolotnikovAbstract:Abstract We consider a bitangential interpolation problem for operator-valued Functions defined on a general class of domains in C n (including as particular cases, Cartan domains of types I–III) which satisfy a type of von Neumann inequality associated with the domain. We show that any such Function has a realization in terms of a unitary colligation and the Defining polynomial for the domain. We show how the solution of various classes of bitangential interpolation problems for this class of Functions corresponds to a unitary extension of a particular partially defined isometry uniquely specified by the interpolation data. Criteria for existence of solutions are given (1) in terms of positivity of a certain kernel completely determined by the data, or, more generally, (2) by the existence of a positive-kernel solution of a certain generalized Stein equation completely determined by the data.