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Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.

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Matrix-order derivatives (differentiating a function a matrix number of times)

I have been exploring methods of generalizing the order of derivatives to a broader range of inputs (such as real numbers, complex, and now matrices). We are very well familiar with integer-order deri …