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In this paper we consider the following problem of phase retrieval: Given a collection of real-valued band-limited functions ${psi_{lambda}}_{lambdain Lambda}subset L^2(mathbb{R}^d)$ that constitutes a semi-discrete frame, we ask whether any real-valued function $f in L^2(mathbb{R}^d)$ can be uniquely recovered from its unsigned convolutions ${{|f ast psi_lambda|}_{lambda in Lambda}}$. We find that under some mild assumptions on the semi-discrete frame and if $f$ has exponential decay at $infty$, it suffices to know $|f ast psi_lambda|$ on suitably fine lattices to uniquely determine $f$ (up to a global sign factor). We further establish a local stability property of our reconstruction problem. Finally, for two concrete examples of a (discrete) frame of $L^2(mathbb{R}^d)$, $d=1,2$, we show that through sufficient oversampling one obtains a frame such that any real-valued function with exponential decay can be uniquely recovered from its unsigned frame coefficients.
We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends
The like-Lebesgue integral of real-valued measurable functions (abbreviated as textit{RVM-MI})is the most complete and appropriate integration Theory. Integrals are also defined in abstract spaces since Pettis (1938). In particular, Bochner integrals
We establish necessary and sufficient conditions for the stability of the finite section method for operators belonging to a certain $C^*$-algebra of operators acting on the Hilbert space $l^2_H(mathbb{Z})$ of $H$-valued sequences where $H$ is a give
In cite{AV99}, Antoine and Vandergheynst propose a group-theoretic approach to continuous wavelet frames on the sphere. The frame is constructed from a single so-called admissible function by applying the unitary operators associated to a representat
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect to this cl