5) we used the Laplace transforms, and by applying the

convolution theorem.

It follows from the classical Titchmarsh

convolution theorem and uniqueness theorem for analytic functions that ker ([K.

By the inverse of a new integral transform and

convolution theorem (33) we find that:

Explanation to Step4: After finding the closeness index blending functions are calculated using

convolution theorem.

b) The

convolution theorem in the theory of two dimensional Laplace transform is given by (see, [2, p.

Alzer [4], who showed that the function g is strictly increasing on (0, [infinity]) by using the

convolution theorem for Laplace transformas.

The

convolution theorem is applied to get the response of the system on temporally Gaussian distributed laser radiation.

9), we take the Laplace transform of its both sides and then apply the well known

convolution theorem for the Laplace transform to the left hand side, we easily obtain the following result with the help of (1.

can be deduced in a manner much like the classical case, as can the abstract version of the

convolution theorem that for each f, g [member of] [L.

The source of this reduction is the

convolution theorem [17], which states that convolution in the SD can be computed as an element-wise product in the FD, in O(N) operations.

Step3: Calculate the blending functions using

convolution theoremSome results like coefficient estimates, growth and distortion theorem, extreme points,

convolution theorem and other interesting properties are investigated.