Imagine the challenge: Take the stage of a vast auditorium before more than a thousand listeners, armed only with a violin -- no orchestra, no piano, nothing to blend in with or hide behind. Make things even tougher by selecting a program that is largely unfamiliar and unremittingly difficult, for both player and listener. Finally, not only keep the vast majority of your audience for the entire concert, but bring it instantly to its feet at the end of a long afternoon, whooping for more.

Maxim Vengerov, who did all of the above at the Kennedy Center Concert Hall Saturday afternoon, is a brave man and a brilliant musician. His program, presented by the Washington Performing Arts Society, was both deeply brainy and spectacularly virtuosic -- a rare combination.

Vengerov's technique would seem to know no difficulties. He hits notes squarely in their center -- nothing but bull's-eyes, all afternoon -- and booms out chordal passages with steady, effortless reserves of sonority more usually associated with the pipe organ. His tone is somewhat austere and he makes no concession to old-world sentiment (indeed, Vengerov's person -- as revealed in his endearingly awkward stage patter -- is more "charming" than his playing). And yet every phrase had the uniquely personal authority of the true artist.

The program began with J.S. Bach's familiar Toccata and Fugue in D Minor, transcribed from organ to violin by Bruce Fox-Lefriche. I was immediately impressed by what I'll call Vengerov's narrative ability -- the way he seized and kept the listener's attention like a storyteller, note by note, phrase by phrase, an absolutely essential quality in such starkly exposed music. He made it sound easy: If Claude Debussy used to hypothesize an ideal piano without hammers, Vengerov played the Toccata as if there were no friction between bow and string.

Eugene-Auguste Ysaye (1858-1931) was not only one of the leading violinists of his time (it was for him that Cesar Franck wrote his celebrated sonata) but a composer of some distinction, and his six solo sonatas -- four of which were played on Saturday -- are much more interesting than they need to be. Showy brilliance is expected, and showy brilliance is delivered; as was once said of Chopin's two books of piano Etudes, the person who can play these can play anything. And yet there is considerable substance in the Sonata No. 2, with its teasing riffing on Bach and chant melody, in the unbridled ferocity of the Sonata No. 3, and in the harmonic fancy of the Sonata No. 6.

Vengerov's Russian compatriot, composer Rodion Shchedrin, was represented by his "Echo Sonata" (1984) -- a brash, sputtering Roman candle of a work that calls upon the full resources of the violin. Indeed, it sometimes seems a catalogue of sound effects -- from mouselike squeaking and scurrying to the tumultuous clatter of torrential rain. My own interest in the piece waned fairly early on, but the "Echo Sonata" offered proof once again, if proof were still needed, that Vengerov can do whatever he wants with his violin. May he return soon and often.

In his Kennedy Center performance, Maxim Vengerov exhibited the uniquely personal authority of a true artist.