I have a 36" Sony trinitron xbr television and the screen is slowly "bowing" or squeezing inward on the left and right of the screen. The tv is great and I don't want to trash. Any ideas? I am comfortable with soldering if I needed to. Please help!

This problem is due to the Drive to the Horizontal amplifier not being sufficient, it is usually a power supply issue, or a component in the actual Horizontal drive circuit is close to failing, This can indeed often be an electrolytic capacitor, (Look for any bulging or swelled/discolored capacitors) going faulty, but it also can be many other things too.
What you need to do is obtain a service manual, for your exact make and model TV, this then has all the troubleshooting steps to perform to isolate and hopefully repair your problem. As with ANY set, one ALWAYS starts at the PSU, and makes sure all those voltages are correct as if they are not, then nothing else can be.
Below is a helpful weblink for your TV. You really need to obtain a service manual, for your exact make and model, before you attempt to service any unit. Contacting Sony direct and asking for one maybe what you need to do. As I have had a search for one, but was unable to find anything.

http://personafile.com/SONY-Television-HDTV-34%22-FD-Trinitron-WEGA-XBR-KD-34XBR970-027242693654.htm