We consider a bounded linear operator A in a Hilbert space with a Hilbert-Schmidt Hermitian component (A−A*)/2i. A sharp norm estimate is established for functions of A nonregular on the convex hull of the spectrum. The logarithm, fractional powers and meromorphic functions of operators are examples of such functions. Our results are based on the existence of a sequence An(n = 1, 2,...) of finite dimensional operators strongly converging to A, whose spectra belongs to the spectrum of A. Besides, it is shown that the resolvents and holomorphic functions of An strongly converge to the resolvent and corresponding function of A.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
We study a new Hermite-type interpolating operator arising in a semi-Lagrangian scheme for solving the Vlasov equation in the 2D phase space. Numerical results on uniform and adaptive grids are shown and compared with the biquadratic Lagrange interpolation introduced in (Campos Pinto and Mehrenberger, 2004) in the case of a rotating Gaussian.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.