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In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with Bessel operator.doi:10.15393/j3.art.2016.3390 fatcat:wv2psmafxjcvplxwbyyh5bc7m4