We investigate the relationship between complex symmetry of composition operators C ϕ f = ∘ induced on classical Hardy space H 2 ( D ) by an analytic self-map open unit disk and its Koenigs eigenfunction. A generalization orthogonality known as conjugate-orthogonality will play a key role in this work. show that if is Schröder map (fixes point ∈ with 0 < | ′ 1 σ eigenfunction, then symmetric on...

For bounded smooth domains the number λ1 is the so-called principal eigenvalue. It has a unique eigenfunction, which is positive, and this eigenfunction is the only positive one (up to normalization). Two main references for this type of results, which are usually called maximum principles, are the books by Walter (1964) and by Protter and Weinberger (1967). Extensions to general bounded non-sm...

We study an eigenvalue problem associated with a reaction-diffusionadvection equation of the KPP type in a cellular flow. We obtain upper and lower bounds on the eigenvalues in the regime of a large flow amplitude A 1. It follows that the minimal pulsating traveling front speed c∗(A) satisfies the upper and lower bounds C1A ≤ c∗(A) ≤ C2A. Physically, the speed enhancement is related to the boun...

We are interested in a nonlinear boundary value problem for (|u′′|p−2u′′)′′ = λ|u|p−2u in [0,1], p > 1, with Dirichlet and Neumann boundary conditions. We prove that eigenvalues of the Dirichlet problem are positive, simple, and isolated, and form an increasing unbounded sequence. An eigenfunction, corresponding to the nth eigenvalue, has precisely n− 1 zero points in (0,1). Eigenvalues of the ...

For most `nice' elliptic boundary value problems there is a general expectation that the rst eigenfunction is unique and of xed sign. And indeed, for second order elliptic di erential equations with Dirichlet boundary conditions such a result holds as a consequence of the maximum principle. It is well known that such a maximum principle does not have a direct generalization to higher order elli...

This article is concerned with conjugacy problems arising in homeomorphisms group, Hom(F ), of non-compact subsets F of normed vector spaces E. Given two homeomorphisms f and g in Hom(F ), it is shown how the existence of a conjugacy may be related to the existence of a common generalized eigenfunction of the associated Koopman operators. This common eigenfunction serves to build a topology on ...

For most `nice' elliptic boundary value problems there is a general expectation that the ̄rst eigenfunction is unique and of ̄xed sign. And indeed, for second order elliptic di®erential equations with Dirichlet boundary conditions such a result holds as a consequence of the maximum principle. It is well known that such a maximum principle does not have a direct generalization to higher order elli...