In 1966 Strichartz received his PhD from Princeton University under Elias Stein with thesis Multipliers on generalized Sobolev spaces. In 1967 he was C.L.E. Moore Instructor at Massachusetts Institute of Technology. He is a professor at Cornell University.
Strichartz works on harmonic analysis (including wavelets and analysis on Lie groups), partial differential equations, and analysis on fractals. Strichartz estimates are named after him due to his application of such estimates to harmonic analysis on homogeneous and nonhomogeneous linear dispersive and wave equations; his work was subsequently generalized to nonlinear wave equations by Terence Tao and others. Strichartz is also known for his analysis on fractals, building upon the work of Jun Kigami on the construction of a Laplacian operator on fractals such as the Sierpinski–Menger sponge.
In 1983 he won the Lester Randolph Ford Award for Radon inversion – variations on a theme. He was elected as a member of the 2017 class of Fellows of the American Mathematical Society "for contributions to analysis and partial differential equations, for exposition, and for service to the mathematical community".
- Differential analysis on fractals: a tutorial. Princeton University Press. 2006.
- "Analysis on Fractals". Notices of the AMS. 46: 1199–1208. November 1999.
- A guide to distribution theory and Fourier transforms. CRC Press. 1994. 2nd edition. World Scientific. 2003.
- The way of analysis. Jones and Bartlett. 2000 .
- "Besicovitch meets Wiener—Fourier expansions and fractal measures". Bull. Amer. Math. Soc. (N.S.). 20 (1): 55–59. 1989. doi:10.1090/s0273-0979-1989-15696-6. MR 0948764.