Hardy spaces for the strip

Abstract

In this paper we shall study Hardy spaces of analytic functions in a strip S. Our main result is on one hand an intrinsic characterization of the spaces and on the second that polynomials are dense. We also present an orthogonal (in H 2 (S)) basis of polynomials.

Local solvability and turning for the inhomogeneous Muskat problem

“…So, not only the slope must be small, also amplitude of the curve plays a role. Both result differs from the results corresponding to the infinite depth case (2). We note that the case with boundaries can also be understood as a problem with different permeabilities where the permeability outside vanishes.…”

“…∂ α z 1 (β) sin(z 1 (β)) sinh(z 2 (β)) (cosh(z 2 (β)) − cos(z 1 (β))) 2 dβ + 1 4π π 0 (̟ p 2 (β) + ̟ p 2 (−β))(−1 + cosh(h 2 ) cos(β)) (cosh(h 2 ) − cos(β)) 2 dβ , (50) and, due to (25),…”

Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

“…We now summarize some facts concerning the Hardy spaces of a strip, a thorough treatment of which has recently been given in [5]. However, most (though not all) of the results below follow immediately by means of conformal mapping from the corresponding results in the unit disc, which are well known.…”

Phase Retrieval for Wide Band Signals

“…Proof. For F ∈ H 2 (D) and z ∈ S, by Theorem 2.1 from [4] we have F (φ(z)) = W 1/2 (z)f (z) and equivalently,…”

“…are given by(4),(5),(6) respectively; • B G is the Blaschke product associated with the set A ∪ (Z(F )\A) for some A ⊂ Z(F ); • S G isthe singular inner function associated with the positive singular measure ν G = ν F + ρ, where ρ is an odd real singular measure; and • O G = U O F where U ∈ N + is an outer function and U = 1/U * on D.…”