Not a chance. You need 6” larger all the way around. And no cabinets can be above any part of the cooking surface. It’s a fire hazard.

It has to be at least the same size and IMO you up the CFM you can do the same size as the cooktop or range but certainly not smaller not to mention it will look awful.

Higher CFM cannot make up for too small a hood. The blower (CFM) can only exhaust what is captured and contained in the hood. Blowers only very minimally 'suck' from outside the hood area. IIRC, the CFM required to overcome a 6" difference (EG, for a 48" hood to perform like a 54") is 7x. So, rather than a 600 CFM system (blower + MUA + ducting) you would need 4200 CFM.

The grease, heat, steam and odor laden plume rising from your range will spread out as it rises. A hood the same size as your range will capture only about 50% of this with the rest spreading throughout your kitchen. The minimum recommended for residential is a hood 6" wider than your range and the same depth.

It all depends on what you cook, how often, and how important it is that grease and odors are removed. Ideally your hood s/b 12" wider and 6" deeper. For our 48" range we are installing a 60" x 30" hood.

Aesthetically, a wider hood also looks much better.

Greater CFM never makes up for lack of adequate capture area. Computational flow dynamics has proved that unequivocally.

"There are hundreds of relevant threads."

:-)

Thanks for valuable input.

The 40 inch vent has two blowers with 1200 CFM ; If the knobs which are on the side can be moved, then but barely, rely the stove will be under hood. This is a dacor distinctive cooktop with 6 burners 46 inches. There is a gap of two inches between the hood on both sides ( hood and cabinet edge).

http://www.dacor.com/products/cooktops/distinctive-gas-cooktops

If the stove can be directly under hood, with the knobs outside and not under hood, may fit.

I fear a communications failure. If the hood were 46 inches and the active part of the cooktop were 40 inches, then recentering the hood over the active part of the cooktop might do, depending on what is being cooked. In any case, there should be no gaps where one cannot clean grease.

Hood is 42 inch, cooktop is 46 inches but has 3 inches of knobs on the side which can be moved sideways. so it will be tight fit

That is not at all doable. Give it up. Get a bigger hood. 54”. That isn’t a matter of opinion about knobs. It’s a fact that it will not cover enough territory and it will be a fire hazard that will not pass inspection if there is one bit of wood over that cooktop.