what is " shopping window " ?
"Dude, I am totally down to go try on a few pairs of jeans right now, but I am letting you know that my shopping window is only about 45 minutes today.

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Agreed with Jura - "window" in this context mean the amount of time available to do something: a window (=space) in your schedule.

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Here "shopping window" means the amount of time he has to do his shopping that day

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it means this person has only 45 minutes to do shopping

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Window Shopping has another meaning too = Do not buy any thing, just explore the market.

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window = opportunity
In this case, her opportunity to go shopping is only 45 minutes.