Expansion of automorphic functions

This paper proposes a method of expansion for automorphic functions on Lie groups, which generalizes the usual Fourier series expansion of automorphic functions on SL₂()/SO(2). Detailed consideration is given to the special case of the expansion of functions on SL₃()/SO(3), which are automorphic with respect to SL₃().Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 116, pp. 119–141, 1982.     

Measure theory and pseudo almost automorphic functions: New developments and applications

In this work, we establish a new concept of weighted pseudo almost automorphic functions using the measure theory. We present new results on weighted ergodic functions like completeness and composition theorems. The theory of this work generalizes the classical results on weighted pseudo almost periodic and automorphic functions. For illustration, we provide some applications for evolution equations which include reaction-diffusion systems and partial functional differential equations.     

Composition of pseudo almost automorphic and asymptotically almost automorphic functions

This paper is concerned with pseudo almost automorphic functions, which are more general and complicated than pseudo almost periodic functions and asymptotically almost automorphic functions. New results, concerning the composition of pseudo almost automorphic functions, are established.     

Perturbation theory for pseudo-inverses

A perturbation theory for pseudo-inverses is developed. The theory is based on a useful decomposition (theorem 2.1) ofB ⁺ -A ⁺ whereB andA arem ×n matrices. Sharp estimates of B ⁺ -A ⁺ are derived for unitary invariant norms whenA andB are of the same rank and B -A is small. Under similar conditions the perturbation of a linear systemAx=b is studied. Realistic bounds on the perturbation ofx=A ⁺ b andr=b=Ax are given. Finally it is seen thatA ⁺ andB ⁺ can be compared if and only ifR(A) andR(B) as well asR(A ^H ) andR(B ^H ) are in the acute case. Some theorems valid only in the acute case are also proved.This work was sponsored in part by The Swedish Institute of Applied Mathematics.     

Joint universality theorems for pairs of automorphic zeta functions

In this paper we establish the joint universality theorems for pairs consisting of the Riemann zeta function, automorphic \(L\) -functions associated with holomorphic Hecke eigen cusp forms, Rankin–Selberg \(L\) -functions, and symmetric square \(L\) -functions.