The Experts below are selected from a list of 20886 Experts worldwide ranked by ideXlab platform
Vadim Mogilevskii - One of the best experts on this subject based on the ideXlab platform.
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Symmetric operators with real defect subspaces of the Maximal Dimension. Applications to differential operators
Journal of Functional Analysis, 2011Co-Authors: Vadim MogilevskiiAbstract:Let H be a Hilbert space and let A be a simple symmetric operator in H with equal deficiency indices d:=n±(A)
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Symmetric operators with real defect subspaces of the Maximal Dimension. Applications to differential operators
Journal of Functional Analysis, 2011Co-Authors: Vadim MogilevskiiAbstract:Abstract Let H be a Hilbert space and let A be a simple symmetric operator in H with equal deficiency indices d : = n ± ( A ) ∞ . We show that if, for all λ in an open interval I ⊂ R , the Dimension of defect subspaces N λ ( A ) ( = Ker ( A ⁎ − λ ) ) coincides with d, then every self-adjoint extension A ˜ ⊃ A has no continuous spectrum in I and the point spectrum of A ˜ is nowhere dense in I. Application of this statement to differential operators makes it possible to generalize the known results by Weidmann to the case of an ordinary differential expression with both singular endpoints and arbitrary equal deficiency indices of the minimal operator.
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symmetric operators with real defect subspaces of the Maximal Dimension applications to differential operators
arXiv: Functional Analysis, 2010Co-Authors: Vadim MogilevskiiAbstract:Let $\gH$ be a Hilbert space and let $A$ be a simple symmetric operator in $\gH$ with equal deficiency indices $d:=n_\pm(A)<\infty$. We show that if, for all $\l$ in an open interval $I\subset\bR$, the Dimension of defect subspaces $\gN_\l(A)(=\Ker (A^*-\l))$ coincides with $d$, then every self-adjoint extension $\wt A\supset A$ has no continuous spectrum in $I$ and the point spectrum of $\wt A$ is nowhere dense in $I$. Application of this statement to differential operators makes it possible to generalize the known results by Weidmann to the case of an ordinary differential expression with both singular endpoints and arbitrary equal deficiency indices of the minimal operator. Moreover, we show in the paper, that an old conjecture by Hartman and Wintner on the spectrum of a self-adjoint Sturm - Liouville operator is not valid.
J. C. Ndogmo - One of the best experts on this subject based on the ideXlab platform.
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Structure of Lie point and variational symmetry algebras for a class of odes
Communications in Nonlinear Science and Numerical Simulation, 2018Co-Authors: J. C. NdogmoAbstract:Abstract It is known for scalar ordinary differential equations, and for systems of ordinary differential equations of order not higher than the third, that their Lie point symmetry algebras is of Maximal Dimension if and only if they can be reduced by a point transformation to the trivial equation y ( n ) =0. For arbitrary systems of ordinary differential equations of order n ≥ 3 reducible by point transformations to the trivial equation, we determine the complete structure of their Lie point symmetry algebras as well as that for their variational, and their divergence symmetry algebras. As a corollary, we obtain the Maximal Dimension of the Lie point symmetry algebra for any system of linear or nonlinear ordinary differential equations.
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Algebraic structure and Maximal Dimension of the symmetry algebra for arbitrary systems of ODEs
arXiv: Classical Analysis and ODEs, 2016Co-Authors: J. C. NdogmoAbstract:It is known for scalar ordinary differential equations, and for systems of ordinary differential equations of order not higher than the third, that their Lie point symmetry algebras is of Maximal Dimension if and only if they can be reduced by a point transformation to the trivial equation $\mathbf{y}^{(n)}$=0. For arbitrary systems of ordinary differential equations of order $n \geq 3$ reducible by point transformations to the trivial equation, we determine the complete structure of their Lie point symmetry algebras as well as that for their variational, and their divergence symmetry algebras. As a corollary, we obtain the Maximal Dimension of the Lie point symmetry algebra for any system of linear or nonlinear ordinary differential equations.
Wen Liu - One of the best experts on this subject based on the ideXlab platform.
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Eigenspaces of symmetric graphs are not typically irreducible
Letters in Mathematical Physics, 2018Co-Authors: Gregory Berkolaiko, Wen LiuAbstract:We construct rich families of Schrodinger operators on symmetric graphs, both quantum and combinatorial, whose spectral degeneracies are persistently larger than the Maximal Dimension of an irreducible representation of the symmetry group.
Ruedi Suter - One of the best experts on this subject based on the ideXlab platform.
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abelian ideals in a borel subalgebra of a complex simple lie algebra
Inventiones Mathematicae, 2004Co-Authors: Ruedi SuterAbstract:Let \(\mathfrak{g}\) be a complex simple Lie algebra and \(\mathfrak{b}\) a fixed Borel subalgebra of \(\mathfrak{g}\). We describe the abelian ideals in \(\mathfrak{b}\) in a uniform way, that is, independent of the classification of complex simple Lie algebras. As an application we derive a formula for the Maximal Dimension of a commutative Lie subalgebra of \(\mathfrak{g}\).
Jun Zhang - One of the best experts on this subject based on the ideXlab platform.
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New Maximal Dimension of invariant subspaces to coupled systems with two-component equations
Communications in Nonlinear Science and Numerical Simulation, 2013Co-Authors: Junquang Song, Shoufeng Shen, Yongyang Jin, Jun ZhangAbstract:Abstract In this paper, new Maximal Dimension of invariant subspaces to coupled systems with two-component equations is estimated under certain conditions. It is shown that if the really coupled operator F = ( F 1 , F 2 ) with orders { k 1 , k 2 } ( k 1 ⩾ k 2 ) preserves the invariant subspace W n 1 1 × W n 2 2 ( 0 n 1 n 2 ) , then there holds n 2 - n 1 ⩽ k 1 , n 2 ⩽ 2 k 1 + k 2 + 1 , where F 2 ∈ F is a nonlinear differential operator and W n q q is the space generated by solutions of a linear ordinary differential equation of order n q , ( q = 1 , 2 ) . Several concrete examples are presented to illustrate the result.