Displaying similar documents to “On the differentiability of functions of an operator”

On peaks in carrying simplices

Janusz Mierczyński (1999)

Colloquium Mathematicae

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A necessary and sufficient condition is given for the carrying simplex of a dissipative totally competitive system of three ordinary differential equations to have a peak singularity at an axial equilibrium. For systems of Lotka-Volterra type that result translates into a simple condition on the coefficients.

Eigensystem of an L 2-perturbed harmonic oscillator is an unconditional basis

James Adduci, Boris Mityagin (2012)

Open Mathematics

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For any complex valued L p-function b(x), 2 ≤ p < ∞, or L ∞-function with the norm ‖b↾L ∞‖ < 1, the spectrum of a perturbed harmonic oscillator operator L = −d 2/dx 2 + x 2 + b(x) in L 2(ℝ1) is discrete and eventually simple. Its SEAF (system of eigen- and associated functions) is an unconditional basis in L 2(ℝ).

Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing

Petr Vaněk, Marian Brezina (2013)

Applications of Mathematics

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We analyze a general multigrid method with aggressive coarsening and polynomial smoothing. We use a special polynomial smoother that originates in the context of the smoothed aggregation method. Assuming the degree of the smoothing polynomial is, on each level k , at least C h k + 1 / h k , we prove a convergence result independent of h k + 1 / h k . The suggested smoother is cheaper than the overlapping Schwarz method that allows to prove the same result. Moreover, unlike in the case of the overlapping Schwarz...

Spectraloid operator polynomials, the approximate numerical range and an Eneström-Kakeya theorem in Hilbert space

Jan Swoboda, Harald K. Wimmer (2010)

Studia Mathematica

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We study a class of operator polynomials in Hilbert space which are spectraloid in the sense that spectral radius and numerical radius coincide. The focus is on the spectrum in the boundary of the numerical range. As an application, the Eneström-Kakeya-Hurwitz theorem on zeros of real polynomials is generalized to Hilbert space.