TY - GEN

T1 - Estimates for the singular numbers of the sandwiched Airy transformation

AU - Sloushch, V.A.

PY - 2016

Y1 - 2016

N2 - Compactness conditions and estimates for the singular values of the sandwiched Airy transform $f\mathbb{A}g$ in $L_{2}(\mathbb{R})$ are investigated for suitable functions $f(x)$, $g(x)$, $x\in\mathbb{R}$. Sufficient conditions for inclusion of the operator $f\mathbb{A}g$ in the Schatten -- von Neumann classes $\mathfrak{S}_{p}$, $p\in(0,2)$, are obtained. In particular, conditions for inclusion of the operator $f\mathbb{A}g$ in the trace class are found.

AB - Compactness conditions and estimates for the singular values of the sandwiched Airy transform $f\mathbb{A}g$ in $L_{2}(\mathbb{R})$ are investigated for suitable functions $f(x)$, $g(x)$, $x\in\mathbb{R}$. Sufficient conditions for inclusion of the operator $f\mathbb{A}g$ in the Schatten -- von Neumann classes $\mathfrak{S}_{p}$, $p\in(0,2)$, are obtained. In particular, conditions for inclusion of the operator $f\mathbb{A}g$ in the trace class are found.

KW - Cwikel type estimates

KW - singular numbers

KW - integral operators

KW - Stark operator

M3 - статья в сборнике материалов конференции

SP - 132

EP - 134

BT - Estimates for the singular numbers of the sandwiched Airy transformation

ER -