Dirac δ function is a generalized function, which is often used in physics to represent the density distribution of ideal models such as particles and point charges. The value of this function is equal to zero at all points except zero, and its integral over the whole domain is equal to 1.
Conceptually speaking, Dirac δ function is a "function": the function value is equal to zero at all points except zero, and its integral over the whole definition domain is equal to 1.
Kroneck δ, that is, Croneker function (also known as Croneker δ function, Kroneck δ, Croneker symbol) δij is a binary function named after German mathematician Leopold Kronecker. The independent variable (input value) of Kronecker function is generally two integers. If they are equal, the output value is 1, otherwise it is 0.
The extended data can not be regarded as a function strictly, because there is no function that meets the above conditions. In mathematics, people introduce the concept of generalized function into this kind of function. In generalized function theory, the exact meaning of δ function should be understood in the sense of integration.
In practical application, the δ function always appears with the integral? . δ distribution has important applications in partial differential equations, mathematical and physical methods, Fourier analysis and probability theory.
Some functions can be considered as approximations of Dirac δ functions, but it should be noted that these functions are all constructed by limits, so they are not strictly Dirac δ functions themselves, but they can be calculated as Dirac δ functions in some mathematical calculations.
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