Jespersen specialized in landscapes and often did paintings of sunsets and rises. He was inspired by the artists Janus la cour and was a pupil of Wilhelm Kyhn. Like them, Jespersen kept a high romantic mood in all his oils. He was especially known for his detailed and romantic landscapes from the Alps and Zealand. Jespersen received numerous art prizes and had exhibited in Denmark, Germany, Paris, Chicago, and Budapest.
- Pupil of Wilhelm Kyhn 1878
- Educated at the Royal Art Academy in 1879
- Kunstner foreningen: 1882-1942
- The world fair in Chicago: 1893
- Antwerpen: 1894
- Paris: 1900
- The Glasgow school artists of Denmark, Chicago: 1895
- Budapest: 1936
- Jespersen received numerous art awards and prices among them was Södring prisen: 1884
- Neuhausens prisen: 1889
- Academy priser: 1890,1895,1896.
- Bronze medallion in Paris: 1900
- Tyrol, Austria: 1886,1887,1888,1890,1895
- Norway: 1894,1915
- Italy: 1896-97
- Germany: 1902
- Sweden: 1905, 1913, 1929
- Switzerland: 1906, 1908, 1913, 1924.
- Paris and London: 1907