Kind Of Integral Operator Research Articles

On Weighted Hadamard-Type Singular Integrals and Their Applications

By means of an expression with a kind of integral operators, some properties of the weighted Hadamard-type singular integrals are revealed. As applications, the solution for certain strongly singular integral equations is discussed and illustrated.

Computational methods for an inverse problem in acoustics

The problem of computing normal velocities on the boundary of a region from pressure measurements on an interior surface is considered. The pressure satisfies the Helmholtz equation and is represented by a single layer potential. Once the density function is found, the normal velocities can be easily computed by applying a second kind of integral operator. The problem of solving for the density function from the interior pressure measurements is ill-posed. Regularization methods using the singular value decompostion and iterative methods, such as the conjugate gradient method for the normal equations, are compared for pressure data with noise. [Work supported by NSF and Cessna Aircraft Company.]

Les operateurs integraux dont le noyau est une covariance

In many fields: signal theory, economics, etc...where random functions are introduced, frequently and naturally we encounter integral operators whose kernels are covariances. Of course the most immediate properties of that particular kind of integral operators have already been published, this allows us to quote them without proofs. But these properties are scattered over, so we have thought useful to present here a synthetic ordered, almost full account of them wihout pretending to originality, howerver hoping that, on some points, we give complements and precise details.