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SUMMARY:Marat Markin (California State University\, Fresno)
DTSTART:20201216T200000Z
DTEND:20201216T210000Z
DTSTAMP:20260420T052916Z
UID:NYC-NCG/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/38/"
 >On the Smoothness of Weak Solutions of an Abstract Evolution Equation wit
 h a Scalar Type Spectral Operator</a>\nby Marat Markin (California State U
 niversity\, Fresno) as part of Noncommutative geometry in NYC\n\n\nAbstrac
 t\nGiven the abstract evolution equation\n\n$$y\\prime (t) = Ay(t)\, \\qua
 d t ≥ 0\, \\hskip2cm (AEE)$$\n\nwith a scalar type spectral operator $A$
  in a complex Banach space\, we find conditions on $A$\, formulated exclus
 ively in terms of the location of its spectrum in the complex plane\, nece
 ssary and sufficient for all weak solutions of the equation\, which a prio
 ri need not be strongly differentiable\, to be strongly infinite different
 iable or strongly Gevrey ultradifferentiable of order $\\beta\\ge 1$\, \ni
 n particular analytic or entire\, on $[0\,\\infty)$ or \n$(0\, \\infty)$. 
 We also reveal certain inherent smoothness improvement effects and show th
 at\, if all weak solutions of the equation are Gevrey ultradifferentiable 
 of orders less than one\, then the operator is necessarily bounded.\n\nIn 
 addition\, we find characterizations of the generation of strongly infinit
 e differentiable and Gevrey ultradifferentiable $C_0$-semigroups by scalar
  type spectral operators.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/38/
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