For an ultraparabolic equation of Kolmogorov type with increasing coefficients depending on the parameter and with degeneration on the initial hyperplane, a fundamental solution of the Cauchy problem is constructed and its properties are investigated. The coefficients of the equation are quite smooth, and their growth depends on the growth of some function. Such properties are important for constructing a fundamental solution of the Cauchy problem for an equation of Kolmogorov type with increasing coefficients depending on the variables of the main group.

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