Elliptic functionally-differential equations with contractions of arguments

The solvability of elliptic functionally-differential equations with compressions of arguments in weight spaces were studied. Boundary value problems for elliptic differential-difference equations and nonlocal boundary value for nonlocal boundary-value problems for elliptic differential equations were also studied. Several theorems were used to prove the solvability of the differential equations. A positive solution to Kato's problem for a large class of operators including, differential-difference operators and functional-differential operators with dilations and compressions of arguments were also obtained.