Convolution operators on groups and multiplier theorems for Hermite and Laguerre expansions
Convolution operators on groups and multiplier theorems for Hermite and Laguerre expansions
Using harmonic analysis on nilpotent Lie groups the following theorem is proved. Let a sequence <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace a Subscript n Baseline right-brace"> <mml:semantics> <mml:mrow> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>a</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>n</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\{ {a_{\text {n}}}\}</mml:annotation> </mml:semantics> </mml:math> …