Interpolation and Complex Symmetry

Complex Symmetric Operators and Applications

We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, selfadjoint extensions of s...

About existence, symmetry and symmetry breaking for extremal functions of some interpolation functional inequalities

The Droste-effect and the exponential transform

In this note we give a correspondence between three kinds of pictures. First, we consider pictures with the “Droste-effect”: a scaling symmetry. These are drawn on a plane with a special point, which is the center of the scaling symmetry. Then we use the complex exponential map to transform these pictures to doubly periodic pictures, commonly known as wallpaper pictures, which are drawn on the ...

Optimizing design of 3D seismic acquisition by CRS trace interpolation

Land seismic data acquisition in most of cases suffers from obstacles in fields which deviates geometry of the real acquired data from what was designed. These obstacles will cause gaps, narrow azimuth and offset limitation in the data. These shortcomings, not only prevents regular trace distribution in bins, but also distorts the subsurface image by reducing illumination of the target formatio...

Generalized complex geometry

Generalized complex geometry encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deformation theory, relation to Poisson geometry, and local structure theory. We also define and study generalized complex branes, which interpolate between flat bundles on Lagrangian submanifold...