Study of a Differential Operator of Heun Type Arising in Fluid Dynamics
نویسندگان
چکیده
The paper studies the non-selfadjoint linear differential operator Ly = d dt ( (1−acos t)y+bsin t dy dt ) acting in the Hilbert space L2(−π,π) that originated from a steady state stability problem in fluid dynamics. The operator L is of Heun type and involves two parameters a,b related to the hydrostatic pressure and capillary properties of the fluid. The results concern (1) the properties of functions in the domain of definition of L , (2) conditions on a,b for the linear span of the Fourier basis {eint} to be core of L , and (3) the matrix representation of the reduced resolvent of L in the Fourier basis. In particular, it is shown that the reduced resolvent is compact and of trace class S1 . Mathematics subject classification (2000): 33E10, 47B10, 34L10.
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