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Let M be a closed manifold. We show that the Kontsevich-Vishik trace, which is defined on the set of all classical pseudodifferential operators on M , whose (complex) order is not an integer greater than or equal to − dim M , is the unique functional which (i) is linear on its domain, (ii) has the trace property and (iii) coincides with the L 2-operator(More)
  • J. Seiler
  • 2005
Inha l t sverze ichnis . Seite I . E in le i tung . . . . . . . . . . . . . . . . . . . . . . . 2 I I . Biologische Beohachtungen . . . . . . . . . . . . . . . . . . 5 1. Allgemeine Einf i ihruug . . . . . . . . . . . . . . . . . . 5 2. Kurze Charakter is t ik der Untersuchungsobjekte . . . . . . . . . 8 a) Solenobia triquelrella F. R . . . . . . . . . . .(More)
I n h a l t s v e r z e i c h n i s . Seite I. E in le i tung . . . . . . . . . . . . . . . . . . . . . . . 81 II . Die zytologischen Beobachtungstatsachen . . . . . . . . . . . . . 83 1. Die haploide Chromosomenzahl . . . . . . . . . . . . . . . 83 a) Samenreifung . . . . . . . . . . . . . . . . . . . . 83 b) Ei re i fang . . . . . . . . . . . . . . . . .(More)
We consider pseudodifferential Douglis-Nirenberg systems on R n with components belonging to the standard Hörmander class S * 1,δ (R n ×R n), 0 ≤ δ < 1. Parameter-ellipticity with respect to a subsector Λ ⊂ C is introduced and shown to imply the existence of a bounded H∞-calculus in suitable scales of Sobolev, Besov, and Hölder spaces. We also admit non(More)
We prove a maximal regularity result for operators corresponding to rotation invariant (in space) symbols which are inhomogeneous in space and time. Symbols of this type frequently arise in the treatment of half-space models for (free) boundary value problems. The result is obtained by extending the Newton polygon approach to variables living in complex(More)
We study closed extensions A of an elliptic differential operator A on a manifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent (λ − A) −1 exists in a sector of the complex plane and decays like 1/|λ| as |λ| → ∞. Moreover, we determine the structure of the resolvent(More)
We derive conditions that ensure the existence of a bounded H∞-calculus in weighted Lp-Sobolev spaces for closed extensions A T of a differential operator A on a conic manifold with boundary, subject to differential boundary conditions T. In general, these conditions ask for a particular pseudodifferential structure of the resolvent (λ − A T) −1 in a sector(More)
A well known result on pseudodifferential operators states that the noncommutative residue (Wodzicki residue) of a pseudodifferential projection vanishes. This statement is non-local and implies the regularity of the eta invariant at zero of Dirac type operators. We prove that in a filtered algebra the value of a projection under any residual trace depends(More)
We study the closed extensions (realizations) of differential operators subject to homogeneous boundary conditions on weighted Lp-Sobolev spaces over a manifold with boundary and conical singularities. Under natural ellipticity conditions we determine the domains of the minimal and the maximal extension. We show that both are Fredholm operators and give a(More)