Diffraction and Dirichlet Problem for Parameter-Elliptic Convolution Operators with Constant Symbols

Diffraction-type problems for parameter-elliptic pseudo-differential operators

“…If the symbols a and b are variable symbols, it is generally impossible to find an exact solution and sometimes one can prove only the existence and uniqueness theorem and indicate a general solution in implicit form. We now state the following theorem, which is the generalisation of the result in [5]:…”

“…We remark tnat specifically if the symbols a and b corresponding to the pseudodifferential operators A and B are constant symbols (independent of x), thie formulas (7) and (9) define the exact solutions to the problems (6) and (8), respectively (see [5]). If the symbols a and b are variable symbols, it is generally impossible to find an exact solution and sometimes one can prove only the existence and uniqueness theorem and indicate a general solution in implicit form.…”

“…We consider the following diffraction problem: AU = f C $j,m,n u C H, (R n)* (6) It follows from [5] that problem (6) …”