Complex powers of classical SG-pseudodifferential operators

Abstract Under a suitable ellipticity condition, we show that classical SG-pseudodifferential operators of nonnegative order possess complex powers. We show that the powers are again classical and derive an explicit formula for all homogeneous components. Keywords: Complex power, Weighted symbols, Noncompact manifolds     

Local radial Phragmén-Lindelöf estimates for plurisubharmonic functions on analytic varieties

We give a sufficient condition for a local radial Phragmén-Lindelöf principle on analytic varieties. This condition is expressed in terms of existence of hyperbolic directions.

     

Nonclassical multidimensional singular integral operators on R + n+1

Banach algebras of certain bounded operators acting on the half-spaceL _p (R ₊ ⁿ⁺¹ ,x ₀ ) (1<p<, –1<<p–1) are defined which contain for example Wiener-Hopf operators, defined by multidimensional singular convolution integral operators, as well as certain singular integral operators with fixed singularities. Moreover the symbol may be a positive homogeneous function only piecewise continuous on the unit sphere. Actually these multidimensional singular integral operators may be not Calderón-Zygmund operators but are built up by those in lower dimensions. This paper is a continuation of a joint paper of the author together with R.V. Duduchava [10]. The purpose is to investigate invertibility or Fredholm properties of these operators, while the continuity is given by definition. This is done in [10] forp=2 and –1<<1, and in the present paper forL _p (R ₊ ⁿ⁺¹ ,x ₀ ) with 1<p< and –1<<p–1.     

Bildung und Kristallstruktur eines dimeren sauerstoffverbrückten Titanaminobisphenoxides

Formation and Crystal Structure of an Oxygen Bridged Titanium Amino Bisphenoxide Di‐(μ‐oxo)‐titan‐bis[aminobisphenoxide] ( 3 ) was obtained by reaction of (i‐Prop)₂TiL* ( 2 ) {L* = O‐4, 6‐(t‐Bu)₂C₆H₂‐2‐CH₂‐[1, 4‐N₂C₅H₁₀]‐2'‐CH₂‐4', 6'‐(t‐Bu)₂C₆H₂O] with water in a molar ratio 1:1 in diethylether. Both i‐Propyl moieties are substituted yielding the dimeric oxygen bridged amino bisphenoxide complex. The six coordinate Ti atoms are a result of Ti—N and Ti—O interactions of the corresponding atoms of the amino bisphenoxide ligand and the bridging O atoms. The central planar Ti₂O₂ ring may be considered as the general structural feature of the title compound: Space group P1¯, Z = 1, lattice dimensions at —60°C: a = 11.6899(4), b = 11.7873(4), c = 12.6462(4) Å, α = 98.070(1), β = 99.660(1), γ = 95.343(1)°, R₁ = 0.0469, wR₂ = 0.1049, GooF = 0.939.     

Nanostructure investigations with the analytical transmission electron microscope

Concerning the conventional TEM-imaging as well as the analytical procedures the capabilities are pointed out: electron diffraction, energy dispersive X-ray spectroscopy (EDXS) and electron energy loss spectroscopy (EELS). The possibilities of investigation of both nanocrystalline materials and multilayers are discussed, accompanied by examples of current investigations: At alloys, produced by intense milling, at single nanocrystals the imaging by diffraction contrast was successful, the analysis has failed because of the sample thickness. By means of energy spectroscopic imaging multilayers from Fe-SiB/NbCu and Fe/Cr as well as Al₂O₃/TiN have been characterized. Received: 15 July 1997 / Revised: 16 February 1998 / Accepted: 21 February 1998