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Alexandru Pirvuceanu's user avatar
Alexandru Pirvuceanu's user avatar
Alexandru Pirvuceanu
  • Member for 6 years, 7 months
  • Last seen more than a week ago
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If $b\in C^1(E, \mathbb{R})$ and $b'$ is compact, then $b$ is weakly continuous — a reference request
comment
If $b\in C^1(E, \mathbb{R})$ and $b'$ is compact, then $b$ is weakly continuous — a reference request
@IosifPinelis sorry, I have just read your post, I had a very long day. I accepted your answer, it fully solved my problem. I didn't expect this to be so straightforward, but I am really grateful for your answer, now I understand how this is proved. Thank you very much for your help!
comment
If $b\in C^1(E, \mathbb{R})$ and $b'$ is compact, then $b$ is weakly continuous — a reference request
@paulgarrett $b'$ associates with each $x\in E$ the Frechet derivative of $b$ at $x$, which we denote by $b'(x)$. I have just added this in my edit, is the notation clear now?
revised
If $b\in C^1(E, \mathbb{R})$ and $b'$ is compact, then $b$ is weakly continuous — a reference request
added 78 characters in body
awarded
 Editor
comment
If $b\in C^1(E, \mathbb{R})$ and $b'$ is compact, then $b$ is weakly continuous — a reference request
@IosifPinelis Thank you, now I realise that this notion may be a bit vague. Does my edit clarify this?
revised
If $b\in C^1(E, \mathbb{R})$ and $b'$ is compact, then $b$ is weakly continuous — a reference request
added 174 characters in body
asked
If $b\in C^1(E, \mathbb{R})$ and $b'$ is compact, then $b$ is weakly continuous — a reference request
comment
The compact embedding of $H^{1/2}_{2\pi}$ in $L^s(0, 2\pi)$
@cs89 thank you for the reference! I decided to accept username's answer because the book he mentioned is more beginner friendly, but I will surely use the reference you gave me to further my knowledge of function spaces.
accepted
The compact embedding of $H^{1/2}_{2\pi}$ in $L^s(0, 2\pi)$
comment
The compact embedding of $H^{1/2}_{2\pi}$ in $L^s(0, 2\pi)$
thank you so much, this book is truly a gem especially for a beginner like me.
awarded
 Scholar
awarded
 Student
asked
The compact embedding of $H^{1/2}_{2\pi}$ in $L^s(0, 2\pi)$
awarded
 Supporter