Integrated cosine functions

Integrated Cosine Functions

In order to the second order Cauchy problem (CP2): x"(t) Ax(t), z(O) z E D(A"), z"(O) y D(A") on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups, interpolation and extrapolation theorems.

Integrated Processes and the Discrete Cosine Transform

A time-series consisting of white noise plus Brownian motion sampled at equal intervals of time is exactly orthogonalised by a discrete cosine transform (DCTII). This paper explores the properties of a version of spectral analysis based on the discrete cosine transform and its use in distinguishing between a stationary time-series and an integrated (unit root) time-series.

Forms, Functional Calculus, Cosine Functions and Perturbation

In this article we describe properties of unbounded operators related to evolutionary problems. It is a survey article which also contains several new results. For instance we give a characterization of cosine functions in terms of mild well-posedness of the Cauchy problem of order 2, and we show that the property of having a bounded H∞-calculus is stable under rank-1 perturbations whereas the ...

Stability for generators of cosine functions

The Group Reduction for Bounded Cosine Functions on Umd Spaces

It is shown that if A generates a bounded cosine operator function on a UMD space X, then i(−A)1/2 generates a bounded C0-group. The proof uses a transference principle for cosine functions.