Is it possible to connect my 2017 macbook air to a studio display?

No.

• The Compatibility section of Studio Display - Technical Specifications includes the line "MacBook Air (2018 or later)".
• MacBook Air (13-inch, 2017) - Technical Specifications says that your Mac has Thunderbolt 2 ports (with the Mini DisplayPort connector) and supports one external monitor with a resolution of up to 3840x2160 pixels.

GlitchDetected wrote:

can i use an adapter instead? will that work?

What part of

• Apple says they are not compatible
• Apple says that your MacBook Air does not support the 5K resolution of the Studio Display
• Your Mac has an older, slower form of Thunderbolt than the one the Studio Display uses

was unclear?

A 5K display like the Studio Display has about 78% more pixels than the highest-resolution (UHD 4K) display that your Mac supports. Pushing all of those pixels requires hardware in the Mac, and a connection that provides a lot of bandwidth between the Mac and the display.

There is an Apple Thunderbolt 3-to-2 adapter, and it is bidirectional. But it's not going to make the Thunderbolt 2 port on your Mac run at Thunderbolt 3 speeds, or upgrade your Intel integrated GPU. That adapter might let you attach a powered Thunderbolt 3 dock to your Mac (useful now that all Thunderbolt 1 and 2 docks have been long discontinued), but there's no point in using it to try to attach a 5K display.

I assume here that you are talking about the current Studio Display, and not about any of the 20+ year old Studio Displays that Apple sold between 1998 and 2004.