SEATTLE — Optimism is a renewable resource at Microsoft.

In 2011, the company, in a belated attempt to catch up with Apple and Google in the smartphone world, announced a partnership with Nokia, the Finnish device maker. “There are other mobile ecosystems,” Nokia and Microsoft executives said in a joint letter at the time. “We will disrupt them.”

Last year, with sales flagging, Microsoft bought Nokia’s handset business for more than $7 billion, aiming to spur better results by more tightly coupling hardware and software.

Still, sales have not materialized. The global market share of the company’s phones was just under 3 percent in the third quarter, lower than the year before. Analysts, long skeptical about Microsoft’s mobile strategy, have largely thrown up their hands. And in perhaps the biggest slight of all, many mobile-app developers, who can make or break mobile technologies by supporting or ignoring them, are paying little or no attention to Windows Phone.

Cue that optimism.

On Wednesday, Microsoft plans to unveil details about Windows 10, a new operating system for PCs, at an event at its headquarters outside Seattle. The operating system, the company says, will help win back developers by allowing them to more easily adapt PC applications to mobile devices. The company hopes it will also increase the availability of applications for — and lift sales of — the company’s smartphones.