Mixing
Complex smooth maps over $(0 , infty) times G$.
$begingroup$
Suppose that $G$ is a linear, compact and connected Lie group and that we have a map
$$ u:(0,infty) times G longrightarrow mathbb{C}$$
Also we suppose that for all $t_{0}in(0,infty)$ the map
$u(t_{0},cdot)$ is in $mathcal{C}^{infty}(G,mathbb{C})$ and for all
$x_{0}in G$ the map $u(cdot , x_{0})$ is $C^{infty}((0,infty), mathbb{C})$.
This implies that $u$ is in $mathcal{C}^{infty}((0 , infty) times G$)? If the answer is no, what additional conditions do I need to have
$u$ is in $mathcal{C}^{infty}((0 , infty) times G$)?
differential-geometry lie-groups smooth-manifolds smooth-functions
asked Jan 27 at 21:28
Pedro ZapataPedro Zapata
242
$endgroup$
add a comment |
$begingroup$
Suppose that $G$ is a linear, compact and connected Lie group and that we have a map
$$ u:(0,infty) times G longrightarrow mathbb{C}$$
Also we suppose that for all $t_{0}in(0,infty)$ the map
$u(t_{0},cdot)$ is in $mathcal{C}^{infty}(G,mathbb{C})$ and for all
$x_{0}in G$ the map $u(cdot , x_{0})$ is $C^{infty}((0,infty), mathbb{C})$.
This implies that $u$ is in $mathcal{C}^{infty}((0 , infty) times G$)? If the answer is no, what additional conditions do I need to have
$u$ is in $mathcal{C}^{infty}((0 , infty) times G$)?
differential-geometry lie-groups smooth-manifolds smooth-functions
asked Jan 27 at 21:28
Pedro ZapataPedro Zapata
242
$endgroup$
add a comment |
$begingroup$
Suppose that $G$ is a linear, compact and connected Lie group and that we have a map
$$ u:(0,infty) times G longrightarrow mathbb{C}$$
Also we suppose that for all $t_{0}in(0,infty)$ the map
$u(t_{0},cdot)$ is in $mathcal{C}^{infty}(G,mathbb{C})$ and for all
$x_{0}in G$ the map $u(cdot , x_{0})$ is $C^{infty}((0,infty), mathbb{C})$.
This implies that $u$ is in $mathcal{C}^{infty}((0 , infty) times G$)? If the answer is no, what additional conditions do I need to have
$u$ is in $mathcal{C}^{infty}((0 , infty) times G$)?
differential-geometry lie-groups smooth-manifolds smooth-functions
asked Jan 27 at 21:28
Pedro ZapataPedro Zapata
242
$endgroup$
Suppose that $G$ is a linear, compact and connected Lie group and that we have a map
$$ u:(0,infty) times G longrightarrow mathbb{C}$$
Also we suppose that for all $t_{0}in(0,infty)$ the map
$u(t_{0},cdot)$ is in $mathcal{C}^{infty}(G,mathbb{C})$ and for all
$x_{0}in G$ the map $u(cdot , x_{0})$ is $C^{infty}((0,infty), mathbb{C})$.
This implies that $u$ is in $mathcal{C}^{infty}((0 , infty) times G$)? If the answer is no, what additional conditions do I need to have
$u$ is in $mathcal{C}^{infty}((0 , infty) times G$)?
differential-geometry lie-groups smooth-manifolds smooth-functions
differential-geometry lie-groups smooth-manifolds smooth-functions
asked Jan 27 at 21:28
Pedro ZapataPedro Zapata
242
asked Jan 27 at 21:28
Pedro ZapataPedro Zapata
242
asked Jan 27 at 21:28
Pedro ZapataPedro Zapata
242
asked Jan 27 at 21:28
Pedro ZapataPedro Zapata
242
asked Jan 27 at 21:28
Pedro ZapataPedro Zapata
242
242
add a comment |
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
});
}
});
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%2f3090138%2fcomplex-smooth-maps-over-0-infty-times-g%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
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.
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%2f3090138%2fcomplex-smooth-maps-over-0-infty-times-g%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
