Mixing
Radial functions and differential operators
0
$begingroup$
i have the following problem.
Consider $f(frac{|x|^2}{2})$ a radial function on $mathbb{R}^2$ where $f:mathbb{R}_+tomathbb{R}$. Then my book says
that
$$Delta f-langle x,nabla frangle$$
is basically the same as
$2xf''(x)+(1-2x)f'(x)$
Can someone elaborate on that or give me an example for $f$ to understand this?
real-analysis geometry differential-geometry
asked Jan 16 at 13:26
stieviestievie
63
$endgroup$
add a comment |
0
$begingroup$
i have the following problem.
Consider $f(frac{|x|^2}{2})$ a radial function on $mathbb{R}^2$ where $f:mathbb{R}_+tomathbb{R}$. Then my book says
that
$$Delta f-langle x,nabla frangle$$
is basically the same as
$2xf''(x)+(1-2x)f'(x)$
Can someone elaborate on that or give me an example for $f$ to understand this?
real-analysis geometry differential-geometry
asked Jan 16 at 13:26
stieviestievie
63
$endgroup$
$begingroup$
Your problem (assuming this is how it was given to you) seems to use a very confusing notation. Which is not rare coming from experienced teacher who forget to be sensitive to students comprehension. Please take a look if noting is missing on the question you are asking. Try to tell if $x$ is meant to be a scalar or a vector. If it's a scalar, then $<x,nabla f>$ is making no sense. If it's a vector then $2xf''(x)$ should not be written like this.
$endgroup$
– Mefitico
Jan 30 at 13:04
$begingroup$
If all this is the original problem, then I can answer explaining why that does not make sense, but despite trying I couldn't figure out by myself what is assumed to make this proposition valid.
$endgroup$
– Mefitico
Jan 30 at 13:04
add a comment |
0
0
0
$begingroup$
i have the following problem.
Consider $f(frac{|x|^2}{2})$ a radial function on $mathbb{R}^2$ where $f:mathbb{R}_+tomathbb{R}$. Then my book says
that
$$Delta f-langle x,nabla frangle$$
is basically the same as
$2xf''(x)+(1-2x)f'(x)$
Can someone elaborate on that or give me an example for $f$ to understand this?
real-analysis geometry differential-geometry
asked Jan 16 at 13:26
stieviestievie
63
$endgroup$
i have the following problem.
Consider $f(frac{|x|^2}{2})$ a radial function on $mathbb{R}^2$ where $f:mathbb{R}_+tomathbb{R}$. Then my book says
that
$$Delta f-langle x,nabla frangle$$
is basically the same as
$2xf''(x)+(1-2x)f'(x)$
Can someone elaborate on that or give me an example for $f$ to understand this?
real-analysis geometry differential-geometry
real-analysis geometry differential-geometry
asked Jan 16 at 13:26
stieviestievie
63
asked Jan 16 at 13:26
stieviestievie
63
asked Jan 16 at 13:26
stieviestievie
63
asked Jan 16 at 13:26
stieviestievie
63
asked Jan 16 at 13:26
stieviestievie
63
63
$begingroup$
Your problem (assuming this is how it was given to you) seems to use a very confusing notation. Which is not rare coming from experienced teacher who forget to be sensitive to students comprehension. Please take a look if noting is missing on the question you are asking. Try to tell if $x$ is meant to be a scalar or a vector. If it's a scalar, then $<x,nabla f>$ is making no sense. If it's a vector then $2xf''(x)$ should not be written like this.
$endgroup$
– Mefitico
Jan 30 at 13:04
$begingroup$
If all this is the original problem, then I can answer explaining why that does not make sense, but despite trying I couldn't figure out by myself what is assumed to make this proposition valid.
$endgroup$
– Mefitico
Jan 30 at 13:04
add a comment |
$begingroup$
Your problem (assuming this is how it was given to you) seems to use a very confusing notation. Which is not rare coming from experienced teacher who forget to be sensitive to students comprehension. Please take a look if noting is missing on the question you are asking. Try to tell if $x$ is meant to be a scalar or a vector. If it's a scalar, then $<x,nabla f>$ is making no sense. If it's a vector then $2xf''(x)$ should not be written like this.
$endgroup$
– Mefitico
Jan 30 at 13:04
$begingroup$
If all this is the original problem, then I can answer explaining why that does not make sense, but despite trying I couldn't figure out by myself what is assumed to make this proposition valid.
$endgroup$
– Mefitico
Jan 30 at 13:04
$begingroup$
Your problem (assuming this is how it was given to you) seems to use a very confusing notation. Which is not rare coming from experienced teacher who forget to be sensitive to students comprehension. Please take a look if noting is missing on the question you are asking. Try to tell if $x$ is meant to be a scalar or a vector. If it's a scalar, then $<x,nabla f>$ is making no sense. If it's a vector then $2xf''(x)$ should not be written like this.
$endgroup$
– Mefitico
Jan 30 at 13:04
$begingroup$
Your problem (assuming this is how it was given to you) seems to use a very confusing notation. Which is not rare coming from experienced teacher who forget to be sensitive to students comprehension. Please take a look if noting is missing on the question you are asking. Try to tell if $x$ is meant to be a scalar or a vector. If it's a scalar, then $<x,nabla f>$ is making no sense. If it's a vector then $2xf''(x)$ should not be written like this.
$endgroup$
– Mefitico
Jan 30 at 13:04
$begingroup$
If all this is the original problem, then I can answer explaining why that does not make sense, but despite trying I couldn't figure out by myself what is assumed to make this proposition valid.
$endgroup$
– Mefitico
Jan 30 at 13:04
$begingroup$
If all this is the original problem, then I can answer explaining why that does not make sense, but despite trying I couldn't figure out by myself what is assumed to make this proposition valid.
$endgroup$
– Mefitico
Jan 30 at 13:04
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3075721%2fradial-functions-and-differential-operators%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
draft saved
draft discarded
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3075721%2fradial-functions-and-differential-operators%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Your problem (assuming this is how it was given to you) seems to use a very confusing notation. Which is not rare coming from experienced teacher who forget to be sensitive to students comprehension. Please take a look if noting is missing on the question you are asking. Try to tell if $x$ is meant to be a scalar or a vector. If it's a scalar, then $<x,nabla f>$ is making no sense. If it's a vector then $2xf''(x)$ should not be written like this.
$endgroup$
– Mefitico
Jan 30 at 13:04
$begingroup$
If all this is the original problem, then I can answer explaining why that does not make sense, but despite trying I couldn't figure out by myself what is assumed to make this proposition valid.
$endgroup$
– Mefitico
Jan 30 at 13:04