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Knots in $S^{2} x S^{1}$ derived from Sym(2, ℝ)

Sang Lee; Yongdo Lim; Chan-Young Park — 2000

Fundamenta Mathematicae

We realize closed geodesics on the real conformal compactification of the space V = Sym(2, ℝ) of all 2 × 2 real symmetric matrices as knots or 2-component links in $S^{2} \times S^{1}$ and show that these knots or links have certain types of symmetry of period 2.

Simultaneous solutions of operator Sylvester equations

Sang-Gu Lee; Quoc-Phong Vu — 2014

Studia Mathematica

We consider simultaneous solutions of operator Sylvester equations $A_{i} X - X B_{i} = C_{i}$ (1 ≤ i ≤ k), where $(A ₁, . . ., A_{k})$ and $(B ₁, . . ., B_{k})$ are commuting k-tuples of bounded linear operators on Banach spaces and ℱ, respectively, and $(C ₁, . . ., C_{k})$ is a (compatible) k-tuple of bounded linear operators from ℱ to , and prove that if the joint Taylor spectra of $(A ₁, . . ., A_{k})$ and $(B ₁, . . ., B_{k})$ do not intersect, then this system of Sylvester equations has a unique simultaneous solution.

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Currently displaying 1 – 8 of 8

Knots in $S^{2} x S^{1}$ derived from Sym(2, ℝ)

Simultaneous solutions of operator Sylvester equations

A Hopf bifurcation of interfaces in a Dirichlet problem.

From a single chain to a large family of submodules.

Distortion theorems for fractional calculus of certain analytic functions with negative coefficients.

Investigation of the stability via shadowing property.

On certain meromorphic functions with positive coefficients.

Geodesics and circles on real hypersurfaces of type $A$ and $B$ in a complex space form.