TY - JOUR
T1 - Growth of solutions of linear differential equations at a logarithmic singularity
AU - Adolphson, A.
AU - Dwork, B.
AU - Sperber, S.
PY - 1982/5
Y1 - 1982/5
N2 - We consider differential equations Y' = AY with a regular singular point at the origin, where A is an n X n matrix whose entries are p-adic meromorphic functions. If the solution matrix at the origin is of the form Y — P exp(θ log x), where P is an n X n matrix of meromorphic functions and θ is an n X n constant matrix whose Jordan normal form consists of a single block, then we prove that the entries of P have logarithmic growth of order n — 1.
AB - We consider differential equations Y' = AY with a regular singular point at the origin, where A is an n X n matrix whose entries are p-adic meromorphic functions. If the solution matrix at the origin is of the form Y — P exp(θ log x), where P is an n X n matrix of meromorphic functions and θ is an n X n constant matrix whose Jordan normal form consists of a single block, then we prove that the entries of P have logarithmic growth of order n — 1.
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U2 - 10.1090/S0002-9947-1982-0648090-9
DO - 10.1090/S0002-9947-1982-0648090-9
M3 - Article
AN - SCOPUS:0013306150
VL - 271
SP - 245
EP - 252
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 1
ER -