A condition for $\hat f$ to be integrable
87119
A positive "Fourier transform" is integrable
34542
If $f$ is integrable then $|f|$ is also integrable
98836
Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$
83676
Condition for continuity of bilinear form
30996
If $\langle Ta, a\rangle \in \mathbb{R}$ for all $a$ then $T$ is self-adjoint
64270
Boundary Condition for Schrödinger Equation in Infinite Range
113385
Example of $f,g: [0,1]\to[0,1]$ and Riemann-integrable, but $g\circ f$ is not?
124061
Prove the reciprocal of a function is integrable if it is bounded
101778
Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
128361
The kernel and range of the powers of a self-adjoint operator
49511
Do we have $\lim_{h\to 0^+}\int_0^\infty|f(t+h)-f(t)|dt=0$?
128457
Show that $T$ is a compact operator
128159
the Riemann integrability of inverse function
115525
Is the pointwise maximum of two Riemann integrable functions Riemann integrable?
105569
If $f$ is integrable in $[a-1,b+1]$, then prove that $\lim \limits_{h\to 0} \ \int_{a}^{b}|f(x+h)-f(x)| ~ dx=0$
16049
Fourier transform of $\int_{-\infty}^{t}f(t)\, dt$
112501
A funtion and its fourier transformation cannot both be compactly supported unless f=0