THE EXPLICIT FORM OF THE FUNDAMENTAL SOLUTION OF ONE PSEUDO-DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS - Бігун, Галина Степанівна; Осипчук, Михайло Михайлович (PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, 2019)
We consider pseudo-differential equation of the form ut ′ = Au + ( a, B)u here a is a vector in R d , B is a pseudo-differential operator with symbol (i | λ | α −2 λ ) d and c > 0 , α ∈ (1,2] are fixed constants. The fundamental λ∈ R solution of this equation is constructed in the form of inverse Fourier transform. Some of its properties investigated.