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hello,

it is possible only by code modification. lines 624-674 of the dhtmlxcalender.js define header buttons. 

You can add event call to the each button here (highlighted lines should be added):

...
  btnClose.onclick = function (e) {
  (e||event).cancelBubble=true;
  self.callEvent("onButtonClick",["close"])
  self.hide();
   
 }
...
 btnMin.onclick = function(e) {
  (e||event).cancelBubble=true;
  self.callEvent("onButtonClick",["minimize"])
  self.minimize();
 }
...
  btnClear.onclick = function(e) {
  (e||event).cancelBubble=true;
  self.con.value = "";
  self.callEvent("onButtonClick",["clear"])  
  self.hide(); 
  }

To attach button event on the page you can use the following aproach:

calendar.attachEvent("onButtonClick",function(type){

if(type=="click") ...

})