- Why is a² + b² ≥ 2ab ?
- A remark on the divergence theorem
- The Cauchy-Schwarz inequality and the Lagrange identity
- On the existence of a metric compatible with a given connection
- A curious identity on the median triangle
- 27 lines on a smooth cubic surface
- Weighted Hsiung-Minkowski formulas and rigidity of umbilic hypersurfaces
- The discrete Gauss-Bonnet theorem
- Why a vector field rotates about its curl?
- A functional inequality on the boundary of static manifolds
tong cheung yu on On the existence of a metric c… Marco Barchiesi on Simple curves with a positive… tong cheung yu on Toric perspective 1 lamwk on Why is a² + b² ≥ 2ab ? Maurice OReilly on Spherical cosine law KKK on Sobolev and Isoperimetric… Anonymous on Sobolev and Isoperimetric… tong cheung yu on On the existence of a metric c… Anonymous on Closed subspaces of a reflexiv… KKK on A curious identity on the medi…
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- Martingale Theory II: Conditional expectation
- Complex analysis - Problem solving strategies.
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- Mean value properties for harmonic functions on Riemannian manifolds
- A note on Obata's theorem
- Mathematics behind JPEG
- Understanding Lagrange multipliers (1)
- The Brunn-Minkowski inequality and the isoperimetric inequality
- Why does a mirror reverse left and right, but not top and bottom?
Author Archives: Ken Leung
Let X be a Banach space. We know that X embeds into its double dual X** as a closed subspace isometrically via defined by and we say that X is reflexive if this embedding is a surjection. One may continue … Continue reading
The following theorem of Fuglede is a classical result in the theory of normal operators. In the proof, one can appreciate how classical analysis are used in solving problems in operator theory through functional calculus. Let be a complex … Continue reading
A real-valued function f on an interval [a, b] is said to have Intermediate Value Property (IVP) if for any number y lying between f(a) and f(b), there exists some such that f(x) = y. Of course everyone learns that if f … Continue reading
Theorem. For any bounded operators A and B on a complex Hilbert space H, it is impossible that AB – BA = I, where I is the identity operator on H. To establish the theorem, we note some elementary results … Continue reading