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SUMMARY:Igor Chyzhykov (University of Warmia and Mazury\, Poland)
DTSTART:20210223T140000Z
DTEND:20210223T150000Z
DTSTAMP:20260422T200946Z
UID:CAvid/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/32/">I
 rregular solutions of complex linear differential equations in the unit di
 sc</a>\nby Igor Chyzhykov (University of Warmia and Mazury\, Poland) as pa
 rt of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbs
 tract\nIt is shown that the order and the lower order of growth are equal 
 for all non-trivial solutions of $f^{(k)}+A f=0$ if and only if the coeffi
 cient $A$ is analytic in the unit disc and $\\log^+ M(r\,A)/\\log(1-r)$ te
 nds to a~finite limit as $r\\to 1^-$.\nA~family of  examples is constructe
 d\, where the order of solutions remain the same while the lower order may
  vary on a~certain interval depending on the irregular growth of the coeff
 icient.\nThese coefficients emerge as the logarithm of their modulus appro
 ximates smooth radial subharmonic functions of prescribed irregular growth
  on a~sufficiently large subset of the unit disc.\nA~result describing the
  phenomenon behind these  examples is also established. En route to\nresul
 ts of general nature\, a~new sharp logarithmic derivative estimate involvi
 ng the lower order of growth is discovered.\nIn addition to these estimate
 s\,\narguments used are based\, in particular\, on the Wiman-Valiron theor
 y adapted for the lower order.\n
LOCATION:https://researchseminars.org/talk/CAvid/32/
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