Cordial Volterra Integral Operators and Equations

摘要: We examine the class of so called cordial Volterra integral operators (Vφu)(t) = ∫0tt−1φ((t−1s)u(s)ds where φ∈L1(0,1) is core Vφ. Such an operator noncompact and possesses a nontrivial spectrum. present formula for spectrum σm(Vφ) Vφ as working in space Cm[0,T], m⩾0, we discuss polynomial solving equation μu = Vφu+f μ∉σm(Vφ), f∈Cm[0,T].