Continuous coefficient representations for singular integral operators with shift (original) (raw)

The main object of the present work is a class of singular integral operators with a shift (which is useful for modeling various situations in applied mathematics). The operators under consideration have piecewise continuous functions as coefficients. The main goal here is to reduce the complexity of these operators by introducing a new class of singular integral operators strongly related with the first ones but having already continuous functions as coefficients (instead of the initial piecewise continuous ones).