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Another approach to mikusinski's validation of heaviside operational calculus

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The interval function which assigns f(b)-f(a) to the interval [a,b] is called the subtracate of f, and is denoted by f The substracate A of the indicial admittance A of a linear time-invariant system provides a natural time-domain transfer function for the system which preserves information about discontinuities in A. These subtracates are used as operators on point functions, and a validation is obtained of Heaviside operational calculus which accommodates dimensional analysis and distinguishes between operators and operands. It is shown that a Stieltjes convolution integral provides a more natural basis for the calculus than a Riemann convolution integral.

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Education, IEEE Transactions on  (Volume:9 ,  Issue: 3 )