ترغب بنشر مسار تعليمي؟ اضغط هنا

Continued fraction expansions of Herglotz-Nevanlinna functions and generalized indefinite strings of Stieltjes type

109   0   0.0 ( 0 )
 نشر من قبل Jonathan Eckhardt
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English
 تأليف Jonathan Eckhardt




اسأل ChatGPT حول البحث

We employ some results about continued fraction expansions of Herglotz-Nevanlinna functions to characterize the spectral data of generalized indefinite strings of Stieltjes type. In particular, this solves the corresponding inverse spectral problem through explicit formulas.



قيم البحث

اقرأ أيضاً

We continue to investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two more model examples of generalized indefinit e strings under rather wide perturbations. In particular, one of these results allows us to prove that the absolutely continuous spectrum of the isospectral problem associated with the two-component Camassa-Holm system in a certain dispersive regime is essentially supported on the set $(-infty,-1/2]cup [1/2,infty)$.
116 - John Weir 2007
We confirm rigorously the conjecture, based on numerical and asymptotic evidence, that all the eigenvalues of a certain non-self-adjoint operator are real.
121 - S. Hassi , H.L. Wietsma 2013
New classes of generalized Nevanlinna functions, which under multiplication with an arbitrary fixed symmetric rational function remain generalized Nevanlinna functions, are introduced. Characterizations for these classes of functions are established by connecting the canonical factorizations of the product function and the original generalized Nevanlinna function in a constructive manner. Also a detailed functional analytic treatment of these classes of functions is carried out by investigating the connection between the realizations of the product function and the original function. The operator theoretic treatment of these realizations is based on the notions of rigged spaces, boundary triplets, and associated Weyl functions.
We show that the classical Hamburger moment problem can be included in the spectral theory of generalized indefinite strings. Namely, we introduce the class of Krein-Langer strings and show that there is a bijective correspondence between moment sequ ences and this class of generalized indefinite strings. This result can be viewed as a complement to the classical results of M. G. Krein on the connection between the Stieltjes moment problem and Krein-Stieltjes strings and I. S. Kac on the connection between the Hamburger moment problem and 2x2 canonical systems with Hamburger Hamiltonians.
75 - Zhentao Lu 2019
In this short note we prove two elegant generalized continued fraction formulae $$e= 2+cfrac{1}{1+cfrac{1}{2+cfrac{2}{3+cfrac{3}{4+ddots}}}}$$ and $$e= 3+cfrac{-1}{4+cfrac{-2}{5+cfrac{-3}{6+cfrac{-4}{7+ddots}}}}$$ using elementary methods. The first formula is well-known, and the second one is newly-discovered in arXiv:1907.00205 [cs.LG]. We then explore the possibility of automatic verification of such formulae using computer algebra systems (CASs).
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا