The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Genkai Zhang - One of the best experts on this subject based on the ideXlab platform.
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Hua operators, Poisson transform and relative discrete series on line bundles over bounded Symmetric Domains
Journal of Functional Analysis, 2012Co-Authors: Khalid Koufany, Genkai ZhangAbstract:Let Ω = G/K be a bounded Symmetric Domain and S = K/L its Shilov boundary. We consider the action of G on sections of a homogeneous line bundle over Ω and the corresponding eigenspaces of G-invariant differential operators. The Poisson transform maps hyperfunctions on S to the eigenspaces. We characterize the image in terms of twisted Hua operators. For some special parameters the Poisson transform is of Szegö type whose image is in a relative discrete series; we compute the corresponding elements in the discrete series.
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Hua operators, Poisson transform and relative discrete series on line bundle over bounded Symmetric Domains
Journal of Functional Analysis, 2012Co-Authors: Khalid Koufany, Genkai ZhangAbstract:Let $D=G/K$ be a bounded Symmetric Domain and $S=K/L$ be its Shilov boundary We consider the action of $G$ with weight $\nu\in\mathbb{Z}$ on functions on $D$ viewed as sections the line bundle and the corresponding eigenspace of $G$-invariant di erential operators. The Poisson transform maps hyperfunctions on the $S$ to the eigenspaces. We characterize the image in terms of Hua operators on the sections of the line bundle. For some special parameter the Poisson transform is of Szegö type mapping into the relative discrete series; we compute the corresponding elements in the discrete series.
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Hua operators and Poisson transform for bounded Symmetric Domains
Journal of Functional Analysis, 2006Co-Authors: Khalid Koufany, Genkai ZhangAbstract:Let $\Omega$ be a bounded Symmetric Domain of non-tube type in $\mathbb{C}^n$ with rank $r$ and $S$ its Shilov boundary. We consider the Poisson transform $\mathcal{P}_sf(z)$ for a hyperfunction $f$ on $S$ defined by the Poisson kernel $P_s(z, u)=\left({h(z, z)^{\frac{n}{r}}}/{|h(z, u)^{\frac{n}{r}} |^2}\right)^{s}$, $(z, u)\times \Omega\times S$, $s\in \mathbb{C}$. For all $s$ satisfying certain non-integral condition we find a necessary and sufficient condition for the functions in the image of the Poisson transform in terms of Hua operators. When $\Omega$ is the type $\mathbf{I}$ matrix Domain in $M_{n, m}(\mathbb{C})$ ($n\leq m$), we prove that an eigenvalue equation for the second order $M_{n, n}-$valued Hua operator characterizes the image.
Francesca Gladiali - One of the best experts on this subject based on the ideXlab platform.
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on a singular eigenvalue problem and its applications in computing the morse index of solutions to semilinear pde s
Nonlinear Analysis-real World Applications, 2020Co-Authors: Anna Lisa Amadori, Francesca GladialiAbstract:Abstract We investigate nodal radial solutions to semilinear problems of type − Δ u = f ( | x | , u ) in Ω , u = 0 on ∂ Ω , where Ω is a bounded radially Symmetric Domain of R N ( N ≥ 2 ) and f is a real function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, which is studied in full detail. The presented approach also describes the symmetries of the eigenfunctions. This characterization enables to give a lower bound for the Morse index in a forthcoming work.
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On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE’s: II*
Nonlinearity, 2020Co-Authors: Anna Lisa Amadori, Francesca GladialiAbstract:By using a characterization of the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem given in Amadori A L and Gladiali F (2018 arXiv:1805.04321), we give a lower bound for the Morse index of radial solutions to Henon type problems where Ω is a bounded radially Symmetric Domain of (N ≥ 2), α > 0 and f is a real function. From this estimate we get that the Morse index of nodal radial solutions to this problem goes to ∞ as α → ∞. Concerning the real Henon problem, f(u) = |u| p−1 u, we prove radial nondegeneracy, we show that the radial Morse index is equal to the number of nodal zones and we get that a least energy nodal solution is not radial.
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On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE’s
Nonlinear Analysis: Real World Applications, 2020Co-Authors: Anna Lisa Amadori, Francesca GladialiAbstract:Abstract We investigate nodal radial solutions to semilinear problems of type − Δ u = f ( | x | , u ) in Ω , u = 0 on ∂ Ω , where Ω is a bounded radially Symmetric Domain of R N ( N ≥ 2 ) and f is a real function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, which is studied in full detail. The presented approach also describes the symmetries of the eigenfunctions. This characterization enables to give a lower bound for the Morse index in a forthcoming work.
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on a singular eigenvalue problem and its applications in computing the morse index of solutions to semilinear pde s
arXiv: Analysis of PDEs, 2018Co-Authors: Anna Lisa Amadori, Francesca GladialiAbstract:We investigate nodal radial solutions to semilinear problems of type \[\left\{\begin{array}{ll} -\Delta u = f(|x|,u) \; & \text{ in } \Omega, \qquad u= 0 & \text{ on } \partial \Omega, \end{array} \right. \] where $\Omega$ is a bounded radially Symmetric Domain of ${\mathbb R}^N$ ($N\ge 2$) and $f$ is a real function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, and describe the symmetries of the eigenfunctions. Next we use this characterization to give a lower bound for the Morse index; in such a way we give an alternative proof of an already known estimate for the autonomous problem and we furnish a new estimate for H\'enon type problems with $f(|x|,u)=|x|^{\alpha} f(u)$. Concerning the real H\'enon problem, $f(|x|,u)=|x|^{\alpha} |u|^{p-1}u$, we prove radial nondegeneracy and show that the radial Morse index is equal to the number of nodal zones.
Khalid Koufany - One of the best experts on this subject based on the ideXlab platform.
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Hua operators, Poisson transform and relative discrete series on line bundles over bounded Symmetric Domains
Journal of Functional Analysis, 2012Co-Authors: Khalid Koufany, Genkai ZhangAbstract:Let Ω = G/K be a bounded Symmetric Domain and S = K/L its Shilov boundary. We consider the action of G on sections of a homogeneous line bundle over Ω and the corresponding eigenspaces of G-invariant differential operators. The Poisson transform maps hyperfunctions on S to the eigenspaces. We characterize the image in terms of twisted Hua operators. For some special parameters the Poisson transform is of Szegö type whose image is in a relative discrete series; we compute the corresponding elements in the discrete series.
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Hua operators, Poisson transform and relative discrete series on line bundle over bounded Symmetric Domains
Journal of Functional Analysis, 2012Co-Authors: Khalid Koufany, Genkai ZhangAbstract:Let $D=G/K$ be a bounded Symmetric Domain and $S=K/L$ be its Shilov boundary We consider the action of $G$ with weight $\nu\in\mathbb{Z}$ on functions on $D$ viewed as sections the line bundle and the corresponding eigenspace of $G$-invariant di erential operators. The Poisson transform maps hyperfunctions on the $S$ to the eigenspaces. We characterize the image in terms of Hua operators on the sections of the line bundle. For some special parameter the Poisson transform is of Szegö type mapping into the relative discrete series; we compute the corresponding elements in the discrete series.
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Hua operators and Poisson transform for bounded Symmetric Domains
Journal of Functional Analysis, 2006Co-Authors: Khalid Koufany, Genkai ZhangAbstract:Let $\Omega$ be a bounded Symmetric Domain of non-tube type in $\mathbb{C}^n$ with rank $r$ and $S$ its Shilov boundary. We consider the Poisson transform $\mathcal{P}_sf(z)$ for a hyperfunction $f$ on $S$ defined by the Poisson kernel $P_s(z, u)=\left({h(z, z)^{\frac{n}{r}}}/{|h(z, u)^{\frac{n}{r}} |^2}\right)^{s}$, $(z, u)\times \Omega\times S$, $s\in \mathbb{C}$. For all $s$ satisfying certain non-integral condition we find a necessary and sufficient condition for the functions in the image of the Poisson transform in terms of Hua operators. When $\Omega$ is the type $\mathbf{I}$ matrix Domain in $M_{n, m}(\mathbb{C})$ ($n\leq m$), we prove that an eigenvalue equation for the second order $M_{n, n}-$valued Hua operator characterizes the image.
Anna Lisa Amadori - One of the best experts on this subject based on the ideXlab platform.
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on a singular eigenvalue problem and its applications in computing the morse index of solutions to semilinear pde s
Nonlinear Analysis-real World Applications, 2020Co-Authors: Anna Lisa Amadori, Francesca GladialiAbstract:Abstract We investigate nodal radial solutions to semilinear problems of type − Δ u = f ( | x | , u ) in Ω , u = 0 on ∂ Ω , where Ω is a bounded radially Symmetric Domain of R N ( N ≥ 2 ) and f is a real function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, which is studied in full detail. The presented approach also describes the symmetries of the eigenfunctions. This characterization enables to give a lower bound for the Morse index in a forthcoming work.
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On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE’s: II*
Nonlinearity, 2020Co-Authors: Anna Lisa Amadori, Francesca GladialiAbstract:By using a characterization of the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem given in Amadori A L and Gladiali F (2018 arXiv:1805.04321), we give a lower bound for the Morse index of radial solutions to Henon type problems where Ω is a bounded radially Symmetric Domain of (N ≥ 2), α > 0 and f is a real function. From this estimate we get that the Morse index of nodal radial solutions to this problem goes to ∞ as α → ∞. Concerning the real Henon problem, f(u) = |u| p−1 u, we prove radial nondegeneracy, we show that the radial Morse index is equal to the number of nodal zones and we get that a least energy nodal solution is not radial.
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On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE’s
Nonlinear Analysis: Real World Applications, 2020Co-Authors: Anna Lisa Amadori, Francesca GladialiAbstract:Abstract We investigate nodal radial solutions to semilinear problems of type − Δ u = f ( | x | , u ) in Ω , u = 0 on ∂ Ω , where Ω is a bounded radially Symmetric Domain of R N ( N ≥ 2 ) and f is a real function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, which is studied in full detail. The presented approach also describes the symmetries of the eigenfunctions. This characterization enables to give a lower bound for the Morse index in a forthcoming work.
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on a singular eigenvalue problem and its applications in computing the morse index of solutions to semilinear pde s
arXiv: Analysis of PDEs, 2018Co-Authors: Anna Lisa Amadori, Francesca GladialiAbstract:We investigate nodal radial solutions to semilinear problems of type \[\left\{\begin{array}{ll} -\Delta u = f(|x|,u) \; & \text{ in } \Omega, \qquad u= 0 & \text{ on } \partial \Omega, \end{array} \right. \] where $\Omega$ is a bounded radially Symmetric Domain of ${\mathbb R}^N$ ($N\ge 2$) and $f$ is a real function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, and describe the symmetries of the eigenfunctions. Next we use this characterization to give a lower bound for the Morse index; in such a way we give an alternative proof of an already known estimate for the autonomous problem and we furnish a new estimate for H\'enon type problems with $f(|x|,u)=|x|^{\alpha} f(u)$. Concerning the real H\'enon problem, $f(|x|,u)=|x|^{\alpha} |u|^{p-1}u$, we prove radial nondegeneracy and show that the radial Morse index is equal to the number of nodal zones.
Nobukazu Shimeno - One of the best experts on this subject based on the ideXlab platform.
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boundary value problems for the shilov boundary of a bounded Symmetric Domain of tube type
Journal of Functional Analysis, 1996Co-Authors: Nobukazu ShimenoAbstract:Abstract In this article the images of the Poisson transform on the degenerate series representations attached to the Shilov boundary of a bounded Symmetric Domain of tube type are considered. We characterize the images by means of second-order differential equations.
