It is proved that Epstein’s zeta-function ζQ(s) related to a positive definite integral binary quadratic form has a zero 1 2 + iγ with T ≤ γ ≤ T + T 5/11+ε for sufficiently large positive numbers T . This improves a classical result of H. S. A. Potter and E. C. Titchmarsh. To Professor K. Ramachandra on his seventieth birthday

This is a continuation of our ”Lecture on Kac–Moody Lie algebras of the arithmetic type” [25]. We consider hyperbolic (i.e. signature (n, 1)) integral symmetric bilinear form S : M × M → Z (i.e. hyperbolic lattice), reflection group W ⊂ W (S), fundamental polyhedron M of W and an acceptable (corresponding to twisting coefficients) set P (M) ⊂ M of vectors orthogonal to faces of M (simple roots)...

and Applied Analysis 3 to be of the limit point or limit circle type is given in 4, 43 . These two papers seem to be the only ones on time scales which are devoted to the Weyl-Titchmarsh theory for the second order dynamic equations. Another way of generalizing the Weyl-Titchmarsh theory for continuous and discrete Hamiltonian systems was presented in 3, 5 . In these references the authors cons...

‎In this manuscript‎, ‎we study various by uniqueness results for inverse spectral problems of Sturm--Liouville operators using three spectrum with a finite number of discontinuities at interior points which we impose the usual transmission conditions‎. ‎We consider both the cases of classical Robin and eigenparameter dependent boundary conditions.

‎In the present paper‎, ‎some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated‎. ‎Uniqueness theorems for the solution of the inverse problem are proved‎, ‎then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.

We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution. Based on this formalism we analize the modifications introduced by the presence of boundaries. Finally, we discuss the concept of environment-induced decohere...

We consider a class of Jacobi matrices with unbounded entries in the so-called critical (double root, Jordan block) case. prove formula which relates spectral density matrix to asymptotics orthogonal polynomials associated it.