Complex smooth maps over $(0 , infty) times G$.












1












$begingroup$


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







share|cite|improve this question









$endgroup$

















    1












    $begingroup$


    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







    share|cite|improve this question









    $endgroup$















      1












      1








      1


      1



      $begingroup$


      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







      share|cite|improve this question









      $endgroup$




      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






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 27 at 21:28









      Pedro ZapataPedro Zapata

      242




      242






















          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


















          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
















          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














          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





















































          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







          Popular posts from this blog

          'app-layout' is not a known element: how to share Component with different Modules

          Image
          0 My application was working fine until I decided to go with lazy loading: So, my shared component looks like this: import { Component, Renderer2 } from '@angular/core'; export interface FormModel { captcha?: string; } @Component({ selector: 'app-layout', templateUrl: './app-layout.component.html', styleUrls: ['./app-layout.css'] }) export class FullLayoutComponent { } app-layout.component.ts I am using this component in my Another component say school-home.component.html like this: <app-layout> </app-layout> and it was working fine until I created a Module school-home.module.ts like this: import { NgModule } from '@angular/core'; import { CommonModule } from '@angular/common'; import { SchoolhomeRoutingModule ...
          Read more

          android studio warns about leanback feature tag usage required on manifest while using Unity exported app?

          Image
          .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box; } 0 This is a simple project showing cubes on Unity, exported to android project and imported on Android studio. On maifest file it showed following warning: Expecting <uses-feature android:name="android.software.leanback" android:required="false" /> tag I have no information about it. And also on default emptyview android project does not use/mention this feature. I know it is required by TV's and such but why its not added by default? Why is this? And Should I concern about it? android unity3d ...
          Read more

          WPF add header to Image with URL pettitions [duplicate]

          Image
          up vote 0 down vote favorite This question already has an answer here: Image source URI requiring authorization 3 answers Add header to all* HTTP requests on a machine 1 answer first of all sorry for my english. Recently I added some security in the backend of my project, and now I need to send a validation code(apiKey) inside the headers to retrieve the images. I have a problem with ALL images in my project that I had attached in my UI. For example, before I had: <Image Height="90" Source="{Binding Video.Thumbnail}"/> Now I need to change my code to create a CUSTOM petition add the apiKey in the header:...
          Read more