๐ฟ^{๐} and operator norm estimates for the complex time heat operator on homogeneous trees
๐ฟ^{๐} and operator norm estimates for the complex time heat operator on homogeneous trees
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German upper X"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">X</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {X}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a homogeneous tree of degree greater than or equal to three. In this paper we study the complex time heat operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper H Subscript โฆ