Transition frequencies of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>lines of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">K</mml:mi><mml:mprescripts/><mml:none/><mml:mn>39</mml:mn></mml:mmultiscripts></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">K</mml:mi><mml:mprescripts/><mml:none/><mml:mn>40</mml:mn></mml:mmultiscripts></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">K</mml:mi><mml:mprescripts/><mml:none/><mml:mn>41</mml:mn></mml:mmultiscripts></mml:mrow></mml:math>measured with a femtosecond laser frequency comb

We report measurements of the transition frequencies $4s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\ensuremath{-}4p\phantom{\rule{0.2em}{0ex}}^{2}P_{1∕2}$ and $4s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\ensuremath{-}4p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$ of the potassium isotopes 39, 40, and 41 through an atomic beam experiment with a fractional uncertainty of about $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$. For frequency calibration, a fs-laser comb referenced to a Cs atomic clock was used. Compared to previous results, hyperfine constants for the states $4p\phantom{\rule{0.2em}{0ex}}^{2}P_{1∕2}$ and $4p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$ and isotope shifts are given with a considerably reduced uncertainty. This paper also resolves the discrepancy of transition frequencies measured by Banerjee et al. [Phys. Rev. A 70, 052505 (2004)] and Scherf et al. [Z. Phys. D 36, 31 (1996)] and the hyperfine constant $A(^{39}\mathrm{K},^{2}P_{1∕2})$ reported by Banerjee et al. [Europhys. Lett. 65, 172 (2004)] and Bendali et al. [J. Phys. B 14, 4231 (1981)].