The most recent business at this address was 103 Grocery & Flower; earlier, according to a onetime resident of the upper Upper West Side, "that place was the Olympia Superette for decades." And earlier than that? The neon lights are long gone, and some of the Art Deco lettering has peeled away, but what remains is strongly suggestive of "Hudes."
This must have been Max Hudes. In 1942, Hudes — "who had operated a takeout-only delicatessen at Broadway and West 103rd Street" and who "wanted a sit-down delicatessen" — became the second owner of the Carnegie Deli, according to How to Feed Friends and Influence People. The book, which doesn't make note of the immediate fate of the sandwich shop, skims quickly over the following decades. With two partners, Hudes operated the Carnegie Deli until 1976.
Also shown: closeups of the Hudes name, revealing still-older lettering, perhaps the beginning of "Broadway," and of the signmaker's indicia. Neonette is long-gone, as are letter telephone exchanges like "EV" ("38"). In full, most likely this was EVergreen 7-1800.
Update: As of September 2014 the signage is no longer visible. Whether it's been effaced or simply covered again is unclear.
Hudes Delicatessen
Surviving signage at 2705 Broadway (103rd-104th Sts.), Manhattan