Definition
The pair of integral equations
where the kernel K(p,r), the auxiliary kernels G(p), g(r) and h(r) are given functions and f(p) is the unknown function to be determined, are called (by a rather ambiguous term) dual integral equations. They mostly appear in the solution of boundary vale problems where the conditions on a boundary line are of mixed type. Therefore we begin our notes giving some simple problems in cylindrical simmetry that historically were the firsts to involve dual integral equations with Bessel type kernels : K(p,r)=Jn(pr). Usually h(r)=0.
The pair of integral equations
where the kernel K(p,r), the auxiliary kernels G(p), g(r) and h(r) are given functions and f(p) is the unknown function to be determined, are called (by a rather ambiguous term) dual integral equations. They mostly appear in the solution of boundary vale problems where the conditions on a boundary line are of mixed type. Therefore we begin our notes giving some simple problems in cylindrical simmetry that historically were the firsts to involve dual integral equations with Bessel type kernels : K(p,r)=Jn(pr). Usually h(r)=0.
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