Phase retrieval(PR) problem is a kind of ill-condition inverse problem which can be found in various of applications. Utilizing the sparse priority, an algorithm called SWF(Sparse Wirtinger Flow) is proposed in this paper to deal with sparse PR problem based on the Wirtinger flow method. SWF firstly recovers the support of the signal and then updates the evaluation by hard thresholding method w...

We construct natural maps (the Klein and Wirtinger maps) from moduli spaces of vector bundles on an algebraic curve X to affine spaces, as quotients of the nonabelian theta linear series. We prove a finiteness result for these maps over generalized Kummer varieties (moduli of torus bundles), leading us to conjecture that the maps are finite in general. The conjecture provides canonical explicit...

We consider the generalized Wirtinger inequality

Phase retrieval (PR) is a kind of ill-condition inverse problem which can be found in various applications. Based on the Wirtinger flow (WF) method, a reweighted Wirtinger flow (RWF) method is proposed to deal with the PR problem. In a nutshell, RWF searches the global optimum by solving a series of sub-PR problems with changing weights. Theoretical analyses illustrate that the RWF has a geomet...

We obtain a sharp estimate for the best constant C > 0 in the Wirtinger type inequality

We discuss the origins of the tangential Cauchy Riemann equation beginning with W. Wirtinger in 1926, and trace the largely unknown early developments until the emergence of the ∂b−Neumann complex in the 1960s. Vienna is a most appropriate venue for a program centered on the ∂− Neumann Problem. Not only did the calculus of the differential operators ∂/∂zj and ∂/∂zj originate in the work of Wilh...

Using Fourier analysis, we derive Wirtinger-type inequalities of arbitrary high order. As applications, prove various sharp geometric for closed curves on the Euclidean plane. In particular, obtain both lower and upper bounds isoperimetric deficit.

The goal of this paper is to extend Poincaré-Wirtinger inequalities from Sobolev spaces to spaces of functions of bounded variation of second order.