Irregular sampling, Toeplitz matrices, and the approximation of entire functions of exponential type

In many applications one seeks to recover an entire function of exponential type from its non-uniformly spaced samples. Whereas the mathematical theory usually addresses the question of when such a function in can be recovered, numerical methods operate with a finite-dimensional model. The numerical reconstruction or approximation of the original function amounts to the solution of a large linear system. We show that the solutions of a particularly efficient discrete model in which the data are fit by trigonometric polynomials converge to the solution of the original infinite-dimensional reconstruction problem. This legitimatizes the numerical computations and explains why the algorithms employed produce reasonable results. The main mathematical result is a new type of approximation theorem for entire functions of exponential type from a finite number of values. From another point of view our approach provides a new method for proving sampling theorems.

     

Reversibler Gleichfeld- und Mikrowellen-Durchschlag in n-Typ-Germanium bei 4,2 °K

The microwave induced breakdown characteristic inn-type germanium at 4.2 °K has been observed and compared with the d.c. induced breakdown characteristic obtained from the same sample. The effective microwave breakdown field intensity is nearly equal to the field intensity observed in d.c. induced breakdown. However, in the breakdown region with conductivities greater than 0.1 ohm^?1 cm^?1 a relaxation effect was found and interpreted qualitatively as momentun relaxation. In the initial breakdown the relaxation time τ _m is small,ω ²τ _m ² being ?1 whereω/2π=9·10⁹s^?1 is the microwave frequency. The relaxation time is determined by predominant neutral impurity scattering with at last 5·10¹⁴ impurities per cm³. This scattering mechanism becomes ineffective when the impurities are ionized by hot carriers. Ionized impurity scattering or acoustic phonon scattering will then be predominant with increased and energy dependent values of τ _m . The increased phase shift between carriers and field causes a decreased energy transfer from the field to the carriers, an accordingly smaller ionization rate, and finally results in a nearly constant a.c. conductivity. The observed anisotropy of the breakdown field intensity is in qualitative agreement with the assumption that only carriers in “hot” valleys of the conduction band initiate the breakdown by impact ionization. The unsufficient quantitative agreement may be due to an inhomogeneity of doping which is suggested by comparing the values of the ohmic low temperature conductivity of the samples.     

Localization of Frames,Banach Frames,and the Invertibility of the Frame Operator

We introduce a new concept to describe the localization of frames. In our main result we show that the frame operator preserves this localization and that the dual frame possesses the same localization property. As an application we show that certain frames for Hilbert spaces extend automatically to Banach frames. Using this abstract theory, we derive new results on the construction of nonuniform Gabor frames and solve a problem about non-uniform sampling in shift-invariant spaces.     

Cyclometalated Iridium(III) and Rhodium(III) Complexes Containing Naphthyridine Ligands: Synthesis,Characterization and Biological Studies

The synthesis, crystal structure, and biological activity of new bis‐cyclometalated compounds [M(ptpy)₂(4‐chloro‐2‐methyl‐1,8‐naphthyridine)]PF₆ [M = Rh ( 1 ); M = Ir ( 2 ); ptpy = 2‐(p‐tolyl)pyridinato] and [M(ptpy)₂(2‐methyl‐1,8‐naphthyridine)]PF₆ [M = Rh ( 3 ); M = Ir ( 4 )] are described. The new compounds were prepared by the reaction of [{M(μ‐Cl)(ptpy)₂}₂] (M = Rh, Ir) with the corresponding naphthyridine ligands. The molecular structures of compounds 1 , 3 , and 4 were confirmed by single‐crystal X‐ray diffraction studies.     

Symbolic Calculus and Fredholm Property for Localization Operators

We study the composition of time-frequency localization operators (wavepacket operators) and develop a symbolic calculus of such operators on modulation spaces. The use of time-frequency methods (phase space methods) allows the use of rough symbols of ultra-rapid growth in place of smooth symbols in the standard classes. As the main application it is shown that, in general, a localization operator possesses the Fredholm property, and thus its range is closed in the target space.     

Spherical goniometry and spacecraft attitude determination

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Spherical goniometry and spacecraft attitude determination