Hi and welcome to Just Answer!
I am sorry for your loss...
If your spouse had no income in 2011 as an executor of his estate you are not required to file a tax return for him.
Because you were married when your spouse died - if that benefits you - you file a joint tax return with your spouse and claim full deductions as for married couple.
If you decide to file a joint tax return - write the word "DECEASED," the decedent's name, and the date of death across the top of the tax return.
If you do not want to file a joint tax return - you may - but are not required to file a separate final tax return for your spouse - put zeros in all field - and there will be zero tax liability. However because your spouse had no income - you are not required to file the tax return for him.
In additional - if your spouse has an estate - and if his estate had any income - such as interest in the bank, pension distributions, etc - you might need to file an income tax return for the estate - let me know if that is your case and I will provide additional information.
Let me know if you need any clarification and if you need any additional help.
I will address all your concerns.