## 🐞 Bug: `.set_spectral_resolution()` not working as expected

[brackham]

Describe the issue
When using Spectrum.set_spectral_resolution() to convolve a high-resolution model spectrum to a lower resolving power, the output does not match the expected behavior:

• It seems to apply the kernel incorrectly, resulting in an over-smoothed or incorrectly broadened spectrum.
• When comparing to a manually implemented log(λ) convolution with scipy.ndimage.gaussian_filter1d, the manual method correctly preserves the resolving power across the wavelength range, while .set_spectral_resolution() does not.

Expected behavior

• For a target constant resolving power R, the convolved spectrum should have a Gaussian LSF with FWHM = λ / R at each wavelength.
• The broadening should appear consistent with how a real instrument works: constant Δλ/λ (constant in log(λ)).

Steps to reproduce

1. Load a high-resolution Spectrum from grid:

   spec = Spectrum.from_grid(teff=4800, logg=4.5, feh=0.0)

2. Call:

   spec_lowres = spec.set_spectral_resolution(500 * u.AA)  # or target_R

3. Plot a sharp feature: compare the width to what’s expected for the desired R.

4. Compare to this working log(λ) Gaussian convolution:

   import numpy as np
   from scipy.ndimage import gaussian_filter1d
   from speclib import Spectrum
   
   def convolve_spectrum_to_R(spec, target_R):
       """
       Convolve a speclib.Spectrum object to a target resolving power R.
       """
       wavelength = spec.wavelength.to("Angstrom").value
       flux = spec.flux.value
   
       log_lambda = np.log(wavelength)
       fwhm_log_lambda = 1.0 / target_R
       sigma_log_lambda = fwhm_log_lambda / (2.0 * np.sqrt(2.0 * np.log(2)))
       dlog_lambda = np.median(np.diff(log_lambda))
       sigma_pixels = sigma_log_lambda / dlog_lambda
   
       flux_smoothed = gaussian_filter1d(flux, sigma_pixels, mode="nearest")
   
       spec_smoothed = Spectrum(
           spectral_axis=spec.wavelength,
           flux=flux_smoothed * spec.flux.unit
       )
   
       return spec_smoothed