THE PROPERTIES OF THE SOLUTIONS OF EQUATIONS SIMILAR TO THE 2-DIMENSIONAL SOBOLEV EQUATION

Two-dimensional analogues of the Sobolev equation P1(D(t))ux1x1(x,t)+P2(D(t))u(x2x2) (x, t) = 0, P(j)(D(t) = SIGMA(K=0)l-1 a(kj)D(t)k+D(t)l, l is-an-element-of N, a(kj) being real constants, are investigated. For equations of this form, we construct a Cauchy-Riemann-type system with operator coefficients, which are convolution operators in t. On the basis of this system, complex-valued functions are introduced, whose properties are similar to those of analytic functions. Analogues of Cauchy's theorem and Cauchy's formula are proved.