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In this paper, we study dissipative q-Sturm—Liouville operators in Weyl’s limit circle case. We describe all maximal dissipative, maximal accretive, self adjoint extensions of q-Sturm—Liouville operators. Using Livšic’s theorems, we prove a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative q-Sturm—Liouville operators.

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Abstract  

By using p-adic q-deformed fermionic integral on ℤp, we construct new generating functions of the twisted (h, q)-Euler numbers and polynomials attached to a Dirichlet character χ. By applying Mellin transformation and derivative operator to these functions, we define twisted (h, q)-extension of zeta functions and l-functions, which interpolate the twisted (h, q)-extension of Euler numbers at negative integers. Moreover, we construct the partially twisted (h, q)-zeta function. We give some relations between the partially twisted (h, q)-zeta function and twisted (h, q)-extension of Euler numbers.

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