RESULTS ON A QUESTION OF ZHANG AND YANG

Abstract For a meromorphic function f,let N(l+1(r,1/f) denote the counting function of zeros of f of order l at least.Let f be a nonconstant meromorphic function,such that (N)(r,f) =S(r,f).Denote F =f...     

PHASE RETRIEVAL OF TIME-LIMITED SIGNALS

The problem of reconstructing a signal ψ(x) from its magnitude |ψ(x)| is of considerable interest to engineers and physicists.This article concerns the problem of determining a time-limited signal f with period 2π when |f(eix)| is known for x ∈ [-π,π].It is shown that the conditions |g(eix)| = |f(eix)| and |g(ei(x+b))-g(eix)| = |f(ei(x+b))-f(eix)|,b = 2π,together imply that either g = wf or g = vf,where both w and v have period b.Furthermore,if 2bπ is irrational then the functions w and v reduce to some constants c1 and c2,respectively;if 2bπ is rational then w takes the form w=eiαB1(eix)B2(eix) and v takes the form ei(x2πN/b+α)B1(eix)B2(eix),where B1 and B2 are Blaschke products.     

SANDWICH-TYPE RESULTS FOR A CLASS OF CONVEX INTEGRAL OPERATORS＊

Let H(U) be the space of analytic functions in the unit disk U.For the integral operator Aφ,(ψ)α,β,γ:K → H(U),with K (C) H(U),defined by Aφ,(ψ)α,β,γ[f](z) =[β+γ/zγφ(z)∫z0fα(t)(ψ)(t)tδ-1 dt]1/β, where α...