Musaev, Hummet K.Shakhmurov, Veli B.2024-05-252024-05-25201671687-277010.1186/s13661-016-0555-12-s2.0-84975721645https://doi.org/10.1186/s13661-016-0555-1https://hdl.handle.net/20.500.14517/170The coercive properties of degenerate abstract convolution-elliptic equations are investigated. Here we find sufficient conditions that guarantee the separability of these problems in L-p spaces. It is established that the corresponding convolution-elliptic operator is positive and is also a generator of an analytic semigroup. Finally, these results are applied to obtain the maximal regularity properties of the Cauchy problem for a degenerate abstract parabolic equation in mixed L-p norms, boundary value problems for degenerate integro-differential equations, and infinite systems of degenerate elliptic integro-differential equations.eninfo:eu-repo/semantics/openAccesspositive operatorsabstract weighted spacesoperator-valued multipliersboundary value problemsconvolution equationsintegro-differential equationsArticleQ1Q2WOS:000391455700001