scholarly journals Spectral expansion series with parenthesis for the nonself-adjoint periodic differential operators

2019 ◽  
Vol 18 (1) ◽  
pp. 397-424 ◽  
Author(s):  
Oktay Veliev ◽  
Keyword(s):  
Differential Operators ◽  
Spectral Expansion ◽  
Expansion Series ◽  
Periodic Differential Operators

Periodic Differential Operators

2013 ◽  
Author(s):  
B. Malcolm Brown ◽  
Michael S.P. Eastham ◽  
Karl Michael Schmidt
Keyword(s):  
Differential Operators ◽  
Periodic Differential Operators

RANK LOWERING OPERATORS ON GL(n, ℝ)

2007 ◽  
Vol 03 (03) ◽  
pp. 365-375
Author(s):  
DORIAN GOLDFELD
Keyword(s):  
Analytic Continuation ◽  
Automorphic Form ◽  
Mellin Transform ◽  
Differential Operators ◽  
Spectral Expansion ◽  
General Rank ◽  
Lowering Operators ◽  
Lowering Operator

If one takes the Mellin transform of an automorphic form for GL(n) and then integrates it along the diagonal on GL(n - 1) then one obtains an automorphic form on GL(n - 1). This gives a rank lowering operator. In this paper a more general rank lowering operator is obtained by combining the Mellin transform with a sum of powers of certain fixed differential operators. The analytic continuation of the rank lowering operator is obtained by showing that the spectral expansion consists of sums of Rankin–Selberg L-functions of type GL(n) × GL(n - 1).

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