ABSTRACT
The proof of some new properties and inversion formulas of the modified kontorovitch-lebedev integral transforms are developed. The parse-val equations for modified kontorovitch-lebedev integral transforms are proved and sufficient conditions for them are found. Some new representations and properties of these transforms are justified. The inequalities which give estimations of these kernels - the real and imaginary parts of the modified Bessel functions of the second kind ReK 1/2+iτ (x) and ImK 1/2+iτ (x) in whole domain of the variable’s alteration x and τ are received.
The new applications of kontorovitch-lebedev transforms to the solution of some mixed boundary value problems in the wedge domains are led. The numerical aspects of using of these transforms are performed properly.
