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 , 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
, 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 theorem
Some results like coefficient estimates, growth and distortion theorem, extreme points, convolution theorem
and other interesting properties are investigated.