TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Euler solutions of pseudodifferential equations
N2  - We consider a homogeneous pseudodifferential equation on a cylinder C = IR x X over a smooth compact closed manifold X whose symbol extends to a meromorphic function on the complex plane with values in the algebra of pseudodifferential operators over X. When assuming the symbol to be independent on the variable t element IR, we show an explicit formula for solutions of the equation. Namely, to each non-bijectivity point of the symbol in the complex plane there corresponds a finite-dimensional space of solutions, every solution being the residue of a meromorphic form manufactured from the inverse symbol. In particular, for differential equations we recover Euler's theorem on the exponential solutions. Our setting is model for the analysis on manifolds with conical points since C can be thought of as a 'stretched' manifold with conical points at t = -infinite and t = infinite.
T3  - Preprint - (1998) 09 
KW  - pseudodifferential operator
KW  - meromorphic family
KW  - residue
Y1  - 2008
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/2317
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-25211
ER  -