Definitions of BSpline

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I can think of 4 ways of defining BSpline with separate, equally spaced knots:

  1. recursion
  2. convolution
  3. sum
  4. divided difference.

Methods 1 & 2 start with the indicator function of the unit interval.

Which of these generalise to nonseparate and/or non-equally spaced knots?

For the case of coallesced knots, can we take as on of our inital BSplines a Dirac delta $\delta(x-t_i)$?