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- W1640806642 abstract "This chapter describes the spaces of generalized functions associated with linear operators. To extend the domains of certain differential operators, several methods have been devised to adjoin elements like δ-functions to spaces of pointwise defined functions. One way of introducing such improper elements is to regard them as continuous linear functionals on a space of test functions equipped with a suitable (metric) topology. They are referred to as distributions. Another way is to define them as generalized functions by a form of weak completion of spaces of test functions. The two methods give the same result; still, there is a fundamental theoretical difference between them. The chapter provides examples to show how classical spaces of distributions may be regarded as generalized elements with respect to specific differential operators." @default.
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- W1640806642 date "1974-01-01" @default.
- W1640806642 modified "2023-10-02" @default.
- W1640806642 title "Spaces of Generalised Functions Associated with Linear Operators" @default.
- W1640806642 doi "https://doi.org/10.1016/s0304-0208(08)70739-4" @default.
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