Holomorphic kernels and commuting operators

Holomorphic Functional Calculi and Sums of Commuting Operators

Let S and T be commuting operators of type ! and type $ in a Banach space X. Then the pair has a joint holomorphic functional calculus in the sense that it is possible to deene operators f(S; T) in a consistent manner, when f is a suitable holomorphic function deened on a product of sectors. In particular, this gives a way to deene the sum S +T when ! +$ <. We show that this operator is always ...

Commuting semigroups of holomorphic mappings

Let S1 = {Ft}t≥0 and S2 = {Gt}t≥0 be two continuous semigroups of holomorphic self-mappings of the unit disk ∆ = {z : |z| < 1} generated by f and g, respectively. We present conditions on the behavior of f (or g) in a neighborhood of a fixed point of S1 (or S2), under which the commutativity of two elements, say, F1 and G1 of the semigroups implies that the semigroups commute, i.e., Ft◦Gs = Gs◦...

HOLOMORPHIC FUNCTIONAL CALCULI AND SUMS OF COMMUTING OPERATORS DAVID ALBRECHT, EDWIN FRANKS AND ALAN McINTOSH

Let S and T be commuting operators of type ! and type $ in a Banach space X . Then the pair has a joint holomorphic functional calculus in the sense that it is possible to de ne operators f(S; T ) in a consistent manner, when f is a suitable holomorphic function de ned on a product of sectors. In particular, this gives a way to de ne the sum S+T when !+$ < . We show that this operator is always...

Commuting holonomies and rigidity of holomorphic foliations

In this article we study deformations of a holomorphic foliation with a generic non-rational first integral in the complex plane. We consider two vanishing cycles in a regular fiber of the first integral with a non-zero self intersection and with vanishing paths which intersect each other only at their start points. It is proved that if the deformed holonomies of such vanishing cycles commute t...

Bergman Kernels and Local Holomorphic Morseinequalitiesrobert