The sectorial projection defined from logarithms

The Bergman Projection on Sectorial Domains

Logarithms and Sectorial Projections for Elliptic Boundary Problems

On a compact manifold with boundary, consider the realization B of an elliptic, possibly pseudodifferential, boundary value problem having a spectral cut (a ray free of eigenvalues), say R − . In the first part of the paper we define and discuss in detail the operator logB; its residue (generalizing the Wodzicki residue) is essentially proportional to the zeta function value at zero, ζ(B, 0), a...

S ep 2 00 7 LOGARITHMS AND SECTORIAL PROJECTIONS FOR ELLIPTIC BOUNDARY PROBLEMS

On a compact manifold with boundary, consider the realization B of an elliptic, possibly pseudodifferential, boundary value problem having a spectral cut (a ray free of eigenvalues), say R − . In the first part of the paper we define and discuss in detail the operator logB; its residue (generalizing the Wodzicki residue) is essentially proportional to the zeta function value at zero, ζ(B, 0), a...

Mining Sectorial Episodes from Event Sequences

In this paper, we introduce a sectorial episode of the form C → r, where C is a set of events and r is an event. The sectorial episode C → r means that every event of C is followed by an event r. Then, by formulating the support and the confidence of sectorial episodes, in this paper, we design the algorithm Sect to extract all of the sectorial episodes that are frequent and confidential from a...

Quasi-sectorial contractions

We revise the notion of the quasi-sectorial contractions. Our main theorem establishes a relation between semigroups of quasi-sectorial contractions and a class of m−sectorial generators. We discuss a relevance of this kind of contractions to the theory of operator-norm approximations of strongly continuous semigroups.