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Is it true that the space of hyperfunctions on $\mathbb{R}^n$ supported at 0 coincides with the space of SchwarzSchwartz distributions supported at 0?

More explicitly, is it true that any hyperfunction supported at 0 is a finite linear combination of various partial derivatives of the delta-function?

If the answer is yes, a reference would be helpful.

Is it true that the space of hyperfunctions on $\mathbb{R}^n$ supported at 0 coincides with the space of Schwarz distributions supported at 0?

More explicitly, is it true that any hyperfunction supported at 0 is a finite linear combination of various partial derivatives of the delta-function?

If the answer is yes, a reference would be helpful.

Is it true that the space of hyperfunctions on $\mathbb{R}^n$ supported at 0 coincides with the space of Schwartz distributions supported at 0?

More explicitly, is it true that any hyperfunction supported at 0 is a finite linear combination of various partial derivatives of the delta-function?

If the answer is yes, a reference would be helpful.

Source Link
asv
asv
  • 21.8k
  • 6
  • 54
  • 121

Hyperfunctions supported at a point

Is it true that the space of hyperfunctions on $\mathbb{R}^n$ supported at 0 coincides with the space of Schwarz distributions supported at 0?

More explicitly, is it true that any hyperfunction supported at 0 is a finite linear combination of various partial derivatives of the delta-function?

If the answer is yes, a reference would be helpful.