16,439 research outputs found
Selberg's orthonormality conjecture and joint universality of L-functions
In the paper we introduce the new approach how to use an orthonormality
relation of coefficients of Dirichlet series defining given L-functions from
the Selberg class to prove joint universality
The Behaviour of the Green Function for the BFKL Pomeron with Running Coupling
We analyse here in LO the physical properties of the Green function solution
for the BFKL equation. We show that the solution obeys the orthonormality
conditions in the physical region and fulfills the completeness requirements.
The unintegrated gluon density is shown to consists of a set of few poles with
parameters which could be determined by comparison with the DIS data of high
precision
Completeness and orthonormality in PT-symmetric quantum systems
Some PT-symmetric non-Hermitian Hamiltonians have only real eigenvalues. There is numerical evidence that the associated PT-invariant energy eigenstates satisfy an unconventional completeness relation. An ad hoc scalar product among the states is positive definite only if a recently introduced "charge operator" is included in its definition. A simple derivation of the conjectured completeness and orthonormality relations is given. It exploits the fact that PT symmetry provides a link between the eigenstates of the Hamiltonian and those of its adjoint, forming a dual pair of bases. The charge operator emerges naturally upon expressing the properties of the dual bases in terms of one basis only, and it is shown to be a function of the Hamiltonian
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