Re: mystery Sobolev space

On Feb 25, 7:52 pm, Stephen Montgomery-Smith
<step...@xxxxxxxxxxxxxxxxx> wrote:
gssprad...@xxxxxxxxx wrote:
Netizens:

What does Hdot^ s, mean, where there is a dot directly above the H? I
think it is some sort of Sobolev space, similar to H^s. In the
context in which I am interested, a function in Hdot^s is a real-
valued function whose domain is the real numbers.

Greg Spradlin
Embry-Riddle University

It's the homogeneous Sobolev space. For example, H^1 are those
functions f for which f and grad f are in L_2. Hdot^1 are those
functions for which grad f is in L_2. It's a bit tricky because you
have to work modulo constants, and for larger s modulo polynomials of
the appropriate degree.

(Hardly a definition, but I hope the example makes it clear.)

This helps. I am concerned with cases where s is negative and not an
integer. Then membership of f in Hdot^s is, I assume, tested by some
condition on the Fourier transform of f. Can anyone flesh this out?

GS
.

Relevant Pages

  • Re: mystery Sobolev space
    ... think it is some sort of Sobolev space, ... It's the homogeneous Sobolev space. ... functions f for which f and grad f are in L_2. ...
    (sci.math)
  • Re: mystery Sobolev space
    ... think it is some sort of Sobolev space, ... It's the homogeneous Sobolev space. ... H^1 are those functions f for which f and grad f are in L_2. ... It's a bit tricky because you have to work modulo constants, and for larger s modulo polynomials of the appropriate degree. ...
    (sci.math)