The Cauchy problem for hyperbolic equations not resolved with respect to the highest time derivative

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Abstract
The first part of the paper focuses on a detailed description of strictly pseudohyperbolic polynomials. The classes of homogeneous and nonhomogeneous polynomials are considered separately. Based on this description, a priori estimates for pseudohyperbolic PDOs with constant coefficients are obtained and the solvability of the Cauchy problem is developed.

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