Two classes of generalized functions used in nonlocal field theory

Two Classes of Generalized Functions Used in Nonlocal Field Theory

We elucidate the relation between the two ways of formulating causality in nonlocal quantum field theory: using analytic test functions belonging to the space S (which is the Fourier transform of the Schwartz space D) and using test functions in the Gelfand-Shilov spaces S α. We prove that every functional defined on S 0 has the same carrier cones as its restrictions to the smaller spaces S α. ...

Nonexistence of two classes of generalized bent functions

We obtain new nonexistence results of generalized bent functions from Z q to Zq (called type [n, q]) in the case that there exist cyclotomic integers in Z[ζq ] with absolute value q n 2 . This result generalize the previous two scattered nonexistence results [n, q] = [1, 2×7] of Pei [13] and [3, 2 × 23] of Jiang-Deng [7] to a generalized class. In the last section, we remark that this method ca...

On Pre-θ-Open Sets and Two Classes of Functions

Zygmund classes in algebras of generalized functions

We introduce an intrinsic notion of Zygmund regularity for Colombeau algebras of generalized functions. In case of embedded distributions belonging to some Zygmund-Hölder space this is shown to be consistent. The definition is motivated by the well-known use of the wavelet transform as a tool in studying Hölder-Zygmund regularity. It is based on a simple mollifier-wavelet interplay which transl...

Two Classes of Special Functions Using Fourier Transforms of Generalized Ultraspherical and Generalized Hermite Polynomials

Mohammad Masjed-Jamei c a, Wolfram Koepf b a Department of Mathematics, K.N.Toosi University of Technology, P.O.Box 16315-1618, Tehran, Iran, E-mail: [email protected] , [email protected] b Institute of Mathematics, University of Kassel, Heinrich-Plett-Str. 40, D-34132 Kassel, Germany, E-mail: [email protected] c School of Mathematics, Institute for Research in Fundamental Science...