On linear homogeneous differential equation of Chebyshev type

Abstract

Let L[y] = y⁽ⁿ⁾(z)+g_n-1(z)y^(n-1)(z)+. . .+g₁(z)y⁽¹⁾(z)+g₀(z)y(z) = 0  be a differential equation of nth order with analytic in circle |z| < R coefficients. We will call above equation by equation of Chebyshev type in |z| < R, if fundamental system of its solution is a Chebyshev system in circle |z| < R . In present paper the conditions with the fulfillment of which the equation L[y] = 0 is of Chebyshev type.