I'm using the following code to create a list of dates:
DateString[#, {"MonthNameShort", ". ", "DayShort"}] & /@
DayRange[{thisyear}, {thisyear, 12, 31}]
How can I change the elements of DateString so that on the first of the month, it only shows the MonthNameShort, and on subsequent days of a month it shows the DayShort?