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14
awarded  Nice Question
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
25
comment Usefulness of alternative constructions of the complex numbers
@BillDubuque Yes, and there are also other constructions, that are in a sense isomorphic. But are they somewhere useful ?
Jun
24
asked Usefulness of alternative constructions of the complex numbers
Jun
24
accepted Varying definitions of symmetric and selfadjoint operators
Jun
24
comment Varying definitions of symmetric and selfadjoint operators
@NateEldredge Thanks for your elaborate edit. Because you put so much work in it and really explain the issue to me, I'm going to award you 50 points
Jun
21
comment Varying definitions of symmetric and selfadjoint operators
Could someone please help me out with this ? I can't accept this answer, until I sort this out.
Jun
18
awarded  Popular Question
Jun
18
comment Varying definitions of symmetric and selfadjoint operators
@NateEldrige [...] Therefore we can in $(\star)$ substitute $A^∗$ for our original $A$ and $D^∗$ for $D$ so that the seld-adjoint requirement becomes $$\left< Au,v\right> =\left< u,Av \right>$$ for all $u,v\in D$, as I wrote in my definition.
Jun
13
comment Varying definitions of symmetric and selfadjoint operators
@NateEldredge I don't quite understand why my definition [B] doesn't match Lax's. I think it's a case of ambiguous wording, but here's how I got to [B] from Lax's definition: We have a fixed set $D$ and an operator $A$ defined on it. Then we construct somehow an set $D^*$ and an operator $A^*$ defined on it, such that by construction $$\left<Au,v\right>=\left<u,A^*v\right>\quad\quad (\star )$$for all $u\in D$ and $v\in D^*$. Then we proceed by calling $A$ self-adjoint, if this construction is such that $D=D^*$ and $A^*=A$, i.e. $D^*$ and $A^*$ equal our initial fixed set and operator. [...]
Jun
12
comment Varying definitions of symmetric and selfadjoint operators
@NateEldredge I updated my question with the according verbatim quotes. Lax indeed seems to defined "symmetric" only for bounded operators - which makes sense, since his "self-adjoint" typically is, as you mentioned, called "symmetric". (I do hope that I haven't mixed up the definitions between the two different books, since these vary in minor details and have wasted your and my time, but a cursory glance does seem to indication that my original transcription isn't flawed.)
Jun
12
asked Varying definitions of symmetric and selfadjoint operators
Mar
30
awarded  Yearling
Jan
31
comment What does “Calculus of Variations in $L^p$ spaces” deal with?
thanks for your detailed answer.
Jan
31
accepted What does “Calculus of Variations in $L^p$ spaces” deal with?
Jan
29
awarded  Popular Question
Jan
29
comment What does “Calculus of Variations in $L^p$ spaces” deal with?
@DavidMitra For different reasons, this option is at the present time (when I have to make the decision of whether to take the course or not) not available to me.
Jan
29
asked What does “Calculus of Variations in $L^p$ spaces” deal with?
Dec
21
awarded  Taxonomist