Kernel theorems for Beurling-Björck type spaces

Beurling-landau-type Theorems for Non-uniform Sampling in Shift Invariant Spline Spaces

Under the appropriate definition of sampling density Dφ, a function f that belongs to a shift invariant space can be reconstructed in a stable way from its non-uniform samples only if Dφ ≥ 1. This result is similar to Landau’s result for the PaleyWiener space B1/2. If the shift invariant space consists of polynomial splines, then we show that Dφ < 1 is sufficient for the stable reconstruction o...

A Beurling-helson Type Theorem for Modulation Spaces

We prove a Beurling-Helson type theorem on modulation spaces. More precisely, we show that the only C changes of variables that leave invariant the modulation spaces M(R) are affine functions on R. A special case of our result involving the Sjöstrand algebra was considered earlier by A. Boulkhemair.

Common Fixed Point Theorems of Integral Type in Modular Spaces

Decomposition Theorems and Kernel Theorems for a Class of Functional Spaces

We prove new theorems about properties of generalized functions defined on Gelfand-Shilov spaces S with 0 ≤ β < 1. For each open cone U ⊂ R we define a space S(U) which is related to S(R) and consists of entire analytic functions rapidly decreasing inside U and having order of growth ≤ 1/(1 − β) outside the cone. Such sheaves of spaces arise naturally in nonlocal quantum field theory, and this ...

Fixed point theorems for new J-type mappings in modular spaces

In this paper, we introduce $rho$-altering $J$-type mappings in modular spaces. We prove some fixed point theorems for $rho$-altering and $rho$-altering $J$-type mappings in modular spaces. We also furnish illustrative examples to express relationship between these mappings. As a consequence, the results are applied to the existence of solution of an integral equation arising from an ODE ...