Modified Green-Hyperbolic Operators

Green Functions Via Hyperbolic Localization

Let G be a reductive algebraic group, with nilpotent cone N and flag variety B. We construct an exact functor from perverse sheaves on N to locally constant sheaves on B, and we use it to study Ext-groups and stalks of simple perverse sheaves on N in terms of the cohomology of B. 2010 Mathematics Subject Classification: Primary 20G05; Secondary 14F05, 32S60.

Representation of Feedback Operators for Hyperbolic Systems

We consider the problem of obtaining integral representation of feedback operators for damped hyperbolic control systems. We show that for the wave equation with Kelvin-Voigt damping and non-compact input operator, the feedback gain operator is Hilbert-Schmidt. This result is then used to provide an explicit integral representation for the feedback operator in terms of functional gains. Numeric...

Schrödinger Operators and Associated Hyperbolic Pencils

For a large class of Schrödinger operators, we introduce the hyperbolic quadratic pencils by making the coupling constant dependent on the energy in the very special way. For these pencils, many problems of scattering theory are significantly easier to study. Then, we give some applications to the original Schrödinger operators including one-dimensional Schrödinger operators with L– operator-va...

Representation Of Feedback Operators For Hyperbolic Systems

On Modified Szasz–mirakyan Operators

We consider certain modifications of Szasz-Mirakyan operators Sn in exponential weighted spaces Cq of continuous functions and operators Tn in L p spaces of Lebesgue integrable functions. We give theorems on approximation properties of these operators. AMS Mathematics Subject Classification (2000): 41A36