We establish precise spectral criteria for potential functions V of reflectionless Schrödinger operators L V = −∂ 2x + V to admit solutions to the Korteweg de-Vries (KdV) hierarchy with V as an initial value. More generally, our methods extend the classical study of algebro-geometric solutions for the KdV hierarchy to noncompact Riemann surfaces by defining generalized Abelian integrals and analogues of the Baker-Akhiezer function on infinitely connected domains with a uniformly thick boundary satisfying a fractional moment condition.

Thiran and Detaille give an explicit formula for the asymptotics of the sup-norm of the Chebyshev polynomials on a circular arc. We give the so-called Szegő-Widom asymptotics for this domain, i.e., explicit expressions for the asymptotics of the corresponding extremal polynomials. Moreover, we solve a similar problem with respect to the upper envelope of a family of polynomials uniformly bounded on this arc. That is, we give explicit formulas for the asymptotics of the error of approximation as well as of the extremal functions. Our computations show that in the proper normalization the limit of the upper envelope represents the diagonal of a reproducing kernel of a certain Hilbert space of analytic functions. Due to Garabedian the analytic capacity in an arbitrary domain is the diagonal of the corresponding Szegő kernel. We don't know any result of this kind with respect to upper envelopes of polynomials. If this is a general fact or a specific property of the given domain, we rise as an open question.

No abstract

Abstract. We raise a conjecture that asymptotics for Chebyshev polynomials in a complex domain can be given in terms of the reproducing kernels of a suitable Hilbert space of analytic functions in this domain. It is based on two classical results due to Garabedian and Widom. To support this conjecture we study asymptotics for Ahlfors extremal polynomials in the complement to a system of intervals on R, arcs on T, and its continuous counterpart.Bibliography: 34 titles.

Φ Abstract -The issue of noise emission from electric drives is becoming increasingly important. Motor manufacturers have to comply with certain standards in order to assure the high competitiveness of their products. At the same time, with today's variable speed drives, which are supplied with nonsinusoidal voltages, the issue of noise reduction has become more complex. This is because the influence of additional factors, compared to machines supplied with sinusoidal voltage, must be considered over a wide speed range. The key to optimizing the machine's acoustic behavior is the thorough knowledge of the influence of the different noise sources and the excitation mechanisms over the complete speed range. Apart from the theoretical analysis and the simulation, an experimental investigation is necessary to obtain a better understanding of the previously mentioned factors and to minimize the machine's acoustic noise. This paper presents some characteristic case studies of acoustic noise emission in asynchronous machines supplied from voltage source inverters in order to examine the influence of diverse factors on the total noise level.