‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

Building on work on Miura’s transformation by Kappeler, Perry, Shubin, and Topalov, we develop a detailed spectral theoretic treatment of Schrödinger operators with matrix-valued potentials, with special emphasis on distributional potential coefficients. Our principal method relies on a supersymmetric (factorization) formalism underlying Miura’s transformation, which intimately connects the tri...

We study short sums of algebraic trace functions via the $q$-analogue van der Corput method, and develop methods arithmetic exponent pairs that coincide with classical case while moduli has sufficiently good factorizations. As an application, we prove a quadratic analogue Brun-Titchmarsh theorem on average, bounding number primes $p\leqslant X$ $p^2+1\equiv0\pmod q$. The other two applications ...

We consider discrete Dirac systems as an approach to the study of corresponding block Toeplitz matrices, which in many ways completes famous via Szegő recurrences and matrix orthogonal polynomials. prove analog Christoffel–Darboux formula derive asymptotic relations for reproducing kernel (using Weyl–Titchmarsh functions systems). These are expressed also terms matrices. case rational (and GBDT...