You can get the Monday of the week for any date by using the following -
|stats count|eval this_mon=now()|eval day=strftime(this_mon,"%u") |eval midtoday=strftime(this_mon,"%m/%d/%Y") |eval me=case(day=1,0,day=2,1,day=3,2,day=4,3,day=5,4,day=6,5,day=7,6)|eval new=me*86400|eval newdate=this_mon-new|eval datething=strftime(newdate,"%b %d %Y")|rename datething as monday
All you need is to change the eval of this_mon to the epoch time of the date you want. For example the above will give you the Monday of the week for the current day. If you wanted, say the Monday for August 12th
|stats count|eval this_mon=strptime("08-12-2015","%m-%d-%Y")|eval day=strftime(this_mon,"%u") |eval midtoday=strftime(this_mon,"%m/%d/%Y") |eval me=case(day=1,0,day=2,1,day=3,2,day=4,3,day=5,4,day=6,5,day=7,6)|eval new=me*86400|eval newdate=this_mon-new|eval datething=strftime(newdate,"%b %d %Y")|rename datething as monday
This is a dummy search using stats count but you can easily inject this into your search and use eval this_mon=_time to use the timestamp of an event.
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