I have recorded, mentally or physically, what you have said. Can also indicate the speaker's annoyance or disinterest. A: "This report needs to be finished by Friday." B: "Duly noted." Your request is duly noted, sir. No red M&Ms in your office. A: "I studied extra hard for this test, Mrs. Smith! I just thought you should know that before you grade them." B: Duly noted. Now close the door on your way out."
See also: noted