Context : Aims : The process of gravitational fragmentation in the L1482 molecular filament of the California molecular cloud is studied by combining several complementary observations and physical estimates . We investigate the kinematic and dynamical states of this molecular filament and physical properties of several dozens of dense molecular clumps embedded therein . Methods : We present and compare molecular line emission observations of the J = 2 - 1 and J = 3 - 2 transitions of ^ { 12 } CO in this molecular complex , using the Kölner Observatorium für Sub-Millimeter Astronomie ( KOSMA ) 3-meter telescope . These observations are complemented with archival data observations and analyses of the ^ { 13 } CO J = 1 - 0 emission obtained at the Purple Mountain Observatory ( PMO ) 13.7-meter radio telescope at Delingha Station in QingHai Province of west China , as well as infrared emission maps from the Herschel Space Telescope online archive , obtained with the SPIRE and PACS cameras . Comparison of these complementary datasets allows for a comprehensive multiwavelength analysis of the L1482 molecular filament . Results : We have identified 23 clumps along the molecular filament L1482 in the California molecular cloud . For these molecular clumps , we were able to estimate column and number densities , masses , and radii . The masses of these clumps range from \sim 6.8 to 62.8 M _ { \odot } with an average value of 24.7 _ { -16.2 } ^ { +31.1 } M _ { \odot } . Eleven of the identified molecular clumps appear to be associated with protostars and are thus referred to as protostellar clumps . Protostellar clumps and the remaining starless clumps of our sample appear to have similar temperatures and linewidths , yet on average , the protostellar clumps appear to be slightly more massive than the latter . All these molecular clumps show supersonic nonthermal gas motions . While surprisingly similar in mass and size to the much better known Orion molecular cloud , the formation rate of high-mass stars appears to be suppressed in the California molecular cloud compared with that in the Orion molecular cloud based on the mass-radius threshold derived from the static Bonnor-Ebert sphere . The largely uniform ^ { 12 } CO J = 2 - 1 line-of-sight velocities along the L1482 molecular cloud shows that it is a generally coherent filamentary structure . Since the NGC1579 stellar cluster is at the junction of two molecular filaments , the origin of the NGC1579 stellar cluster might be merging molecular filaments fed by converging inflows . Our analysis suggests that these molecular filaments are thermally supercritical and molecular clumps may form by gravitational fragmentation along the filament . Instead of being static , these molecular clumps are most likely in processes of dynamic evolution . Conclusions :